There is two ways to approach this hint:

The first way is the most likely easier one as it is more straightforward. The key word for this way is "Victory!". Victory you have after a battle, while already throwing an eye on the rest of the hint it may imply a bit that it has to be about a greater battle, but even if you go through all battles fought in Middle-earth you will only get to one solution.
The greatest battles in Middle-earth of the Third Age are:

- Battle of Five Armies
- Battle of Helms Deep
- Battle of the Pelennor Fields (Minas Tirith)
- Battle of the Morannon (Black Gate)

In the Battles of Five Armies and Helms Deep are no distinct heroes to be praised afterwards. Okay Gimli killed his 42 Orcs in Helms Deep, but others did their part too and maybe had a very similar kind of personal success.

The Battle on the Pelennor Fields was not really celebrated as the enemy was not entirely conquered yet and they straightly moved on to discuss what there is to do next.

This leads to the Battle of the Morannon. You can now argument that the Black Gate is not built yet, but that's not a problem, because we look for the place where it was celebrated (keyword "praise"). We also have very distinct heroes, not from the battle itself but from what the purpose of the battle was: To make it possible for Frodo and Sam to destroy the One Ring unnoticed. These two are the "heroes".

The last difficulty now is that the location we look for only appears in the books. The celebration was not in Minas Tirith, there "only" was the coronation of Aragorn. If you look up the tolkiengateway article for Frodo Baggins however you will get the name of the location you look for: The Field of Cormallen. The last small difficulty is to find out where it is because theres no warp.

Lastly, the "golden circle" part is simply the translation of "Cormallen" (cor = ring, mallen = golden).


The second way to approach the hint is via the keyword "golden". This of course leads to Lothlórien. Lothlórien is golden because of the Mallorn-trees. Looking up more locations with Mellyrn in Middle-earth does not yield much beside the one Sam plants near Bagend in the Fourth Age. The trick then was to look up whether there's more plants that are golden. This may lead to this article: List of Middle-earth plants - Wikipedia, the free encyclopedia. In here you will find the "Culumalda" and right below it the name "Fields of Cormallen".

This again leads to a location not really appearing in the movies, but even with only movie knowledge this one should have been solvable.

If you look up "Corsairs" on tolkiengateway you'll be immidiately redirected to the page of the Corsairs of Umbar. Not much is known about them so it's easy to find the note about the War of the Ring: Aragorn captured their ships (with the army of the Dead) and rowed them to Minas Tirith. Now, Minas Tirith does not have a river right in front of it. There is a separate town which was used as the port of Minas Tirith. This location is known as Harlond, which is where you will find the egg.

The keywords "Three" and "power" hopefully lead you to the Three Elven Rings of Power Narya, Nenya and Vilya. The story that now lies behind this hint is not so well-known, and the name of the location you seek does not appear in the movies nor the books, at least not by name. But research should pretty soon lead to only one location that is connected to all Three Rings: The place where they were forged, the city of Ost-in-Edhil, more concretely the Forge of Ost-in-Edhil.
More information on why these rings destroyed Ost-in-Edhil can be found here: Sack of Eregion - Tolkien Gateway

The "countless pages of knowledge" are hopefully easily read as "many books", which again is to be read as "library". "Covered in dust and rubble" of course is to be read that the place has been destroyed. To have a library the location has to be quite big, as that's not really an essential feature for a town to survive. In fact, as far as I am aware, only one city on MCME features a library: Osgiliath. If you don't know that you can also get to that city: While "dust" implies that it may be an old location, it's "rubble" that probably hints to a non-"natural" or time-driven destruction, but instead a forceful one. This way you can at least break down to relevant cities to Fornost and Osgiliath, that are built on MCME.
When inside Osgiliath it is a bit tedious finding the Library of Osgiliath, but eventually you'll find the big, 3-winged building with a broken dome in the western part of Osgiliath.

This hint unites two lesser known LotR facts (not sure whether either of these appears in the movies, it may be though). Interpreting either of these the right way leads you to the egg:
1. (Thunderstorm) When Gandalf the White meets Aragorn, Gimli and Legolas in Fangorn he tells them about the battle against the Balrog, he notes that from afar the fight may well have looked like a fierce thunderstorm, after two days he managed to defeat the Balrog.
2. In Moria Gandalf mentiones the Endless Stairs, and Gimli responds that most believed it was only a legend and that many speculate it never existed. While chasing the Balrog up these stairs, and during the fight at Durin's Tower these got destroyed.

Standing ontop of Durin's Tower, going down will lead to Moria. On MCME this of course means to switch to moria world. The "fourth of its kind" points to the Fourth Hall of Moria (non-canon assignment), respectively "where once sat the mightiest of his folk" points to the throne room (audition hall) of Moria (non-canon also). The hall is from /warp khazad straight forward (2nd hall -> 3rd hall -> 4th hall).
So the egg is below the throne in the 4th hall of /mvtp moria.

The first thought usually was the Council of Elrond, but if you count through the races involved there - Men, Elves, Dwarves, Hobbits and Maiar, you'll only get five, and not six. Also the meetings in Rivendell were not really unforeseen or surprising, Frodo rested in Rivendell for two months, so I guess the meeting was announced at least some days ahead.
A meeting does not have to be scheduled, a meeting already exists whenever two parties meet without expecting it. So intuitively you can approach this question by brainstorming situations (book or movie) where exactly that happens, nota bene, twice after each other in a short period of time.
Approaching the hint in a more prudential way may be to find out what the sixth race may be. Given that there are no two unforeseen battles happening after each other, you can exclude evil races. This may very soon lead to that it is Ents that are the missing race, and with that the area you have to consider has already shrunk massively. But before you start sifting through entire Fangorn you should think again, which place you are looking for. Of course it can only be what we know as "Treebeard's Hill", where Merry and Pippin met Treebeard and Aragorn and Co. met Gandalf.

Okay, this is some lore from the Silmarillion which probably many do not know about. BUT. It is still possible to find the egg:
"sunk all that surrounds me" = everything around me is water now = island. Makes sense? I hope so. Now there's still quite a bunch of islands on the map, many in river deltas, Carrock, Girdley island, some along the shores, and some in the far north west. The hint to find out which island it is you get by researching for "ever-cold"; I tried it: googling for "Middle-earth island ever-cold" yields the Tolkiengateway article of Himring very far up. Yeah some flying involved, but you won't be dissapointed

The keywords here of course are "only one can persist"; I observed many that flew right away to that dome in Pelargir that was made as a contest build. But still they kept searching for hours after that.
There's many domes in Pelargir, okay, but all of them can persist! The location you look for is a location where only one of many domes can persist = remain on the main map. It requires some out of the box thinking, eventually you may find that the dome you look for is the winning entry for the Pelargir Dome Contest on plotworld.
How to get there: /mvtp plotworld, /warp Plot 2

I hope at least this one did not cause too many headaches . "wet and smelly" points to maybe a swamp or some sewers, with "dwelling" it must be the sewers. Ost-in-Edhil has some kind of underground water system but it's rather not a sewer^^. Thus it gotta be the sewers of Osgiliath. There's an entrance outside the wall a bit down the Anduin.

To start with this one, grasp on the "Still it exists on here", reading it as "it is on the Middle-earth map". Enable warps on the dynmap and scan it for some locations you probably never heard of. Search along the sea shores as the hint suggests.
The town you look for is called Udul, it's sister-town. Udul and its neighbourtown Agar are rivals, at least so far the official lore, I think @Ardelenia pointed out that in server internal lore this was no longer the case, but I have to admit I did not hear anything about that thus far.
The "Where it lies was never told" refers to the fact that Tolkien never settled where these two towns now should be, he proposed various places along the entire shore between the mouths of Isen and Anduin.

The only real difficulty here is to grasp that "King of the Second Line" must refer to the Kings of Rohan. Then it should not be that hard to look up the last King of the Second line (Théoden), then his father (Thengel), his grandfather (Fengel), and his great-grandfather (Folcwine). Then look up the sons of Folcwine: Folcred, Fastred, and ofc. Fengel again. Then look into the story of these three and you soon will find that the twin brothers Folcred and Fastred died in a battle at the Fords of Poros and are also buried there in a place known as Haudh in Gwanûr.

There are many dwellings with walls, floor and ceiling out of stone, Moria, or any house with stony materials, so you probably should investigate on the inhabitant(s). Turning to stone is something quite unusual I would say, and they even appear both in the Hobbit and the Lord of the Rings, so reflecting what you read/saw there should hopefully lead you to Tom, Bert and William Huggins, the stone Trolls of Bilbo. Remember the scene in the LotR movie when he tells that story to the Hobbit children? Yes? See, I knew you would know all you need to find this egg .

Nope this is not a reference to the dwarf-song from the Hobbit, there the trees themselved burned, which is not the case here. Maybe a good question is to ask yourself where there are red trees on the map; too bad dynmap is not showing that . Entire Anfalas has red trees, but remember the #1 tip: The hint points to a very specific location! You also are looking for a location that somehow has something to do with fire, too bad this is not recognisable on dynmap either, so if you did not know about this location before you gotta search a bit.
Your search hopefully leads you to Lindemar, a non-canonical town in the Morthond valley, on the southern slopes of the White Mountains in Gondor. The town got victim to a severe fire and many houses have burned down. The name is Quenya and means, you can guess, "home of the singer". The location was devoted to Sir Christopher Lee who played Saruman in the LotR and Hobbit movies, and was also a singer.

My #1 tip for this one: It's a really silly one, don't think too far. Many did think very far, interpreted it as chapter 7 of the Hobbit (would have pointed to Beorn's House which is not built yet though), and even Henry the 7th, and many more creative approaches.
The right interpretation approach would have been "a field on a chessboard", "a square on a map", or the code for a Plotbuild Plot. Now dynmap is your friend, and you don't need to study the plotworld map for very long to find the big grid labelled with letters and roman numerals.

The "Last home" of a person usually is where he is buried. At that point I have to admit that it is not entirely clear where exactly the Princes of Cardolan are buried, but what is pretty clear is that it was somewhere in the Barrow Downs. Where exactly in the Barrow Downs I therefore tried to point out with the keywords "many rooms" = big barrow. There is one barrow to which we usually refer to as "Great Barrow", it's in the southern Barrow Downs, a bit north of the Greenway from Bree.

"Very different in appearance" points to that the site you're looking for is still well preserved/maintained and not haunted but much more well guarded and of high esteem. Something like this you will find not in many places, and the most iconic of them is the Hallows of Minas Tirith. The egg is inside the domed ceremony building.

I was very surprised about how hard this egg still proofed, but let's unravel it
"Only one fiery mountain in Middle-earth, but many more elsewhere". So far we had an egg in the Moria world and two in Plotworld, and this is by far the most clear hint that this egg also is not on the main map! So many started with the "grandfather of Legolas" (which is Oropher) and started searching in Mirkwood... Are there any fiery mountains there? No. So why searching there then?
To find the many fiery mountains in an other world than the main map you best use Dynmap. On Plotworld you wont find many fiery mountains either, and ofc neither on moria map, and neither on the old map. So all that is left is the Themed Build world. ("The grandfather of Oropher has claimed ownership over the one you seek", also a pretty clear hint towards TB world, ain't it?). The right TB can be found pretty easily, and if you enable warps you'll see that there is /warp theme close by.
The egg is in the Sammath Naur TB on the plot of user Oropher_.

This is in my opinion the hardest one. The hint given is a very specific lore fact that is only mentioned in the Unfinished Tales of Númenor and Middle-earth, and there it is not given in the form L*ND*L but rather described as "a black stone with 3 letters engraved: lambë, ando, lambë", the are names of elvish letters, representing the sounds L, ND and L again, so the insription actually looks like this:

The stone is located at the Tomb of Elendil on Amon Anwar, also known as Halifiren, the Beacon Hill at the border of Gondor and Rohan. I guess the only way to get to this is by speaking the three consonants aloud and guess that the proper word may be "Elendil".

The first thought here is usually the Seven Dwarven Rings. But can rings see? If you cant directly think of an item that once existed seven times, try thinking of something that at least exists multiple times. It is a very iconic item both in movies and book: The Palantíri. Look them up and you will find the piece of information you will need: The Elendil-Stone was the only one that could see across the Great Sea to the shores of the Undying Lands. The stone is located in the Tower of Elostirion in the Tower Hills, West of the Shire.