Since the end of the First Age, Melian the Maia dwells in Lorien that in Valinor and mourns over her beautiful days with Thingol in Doriath, that are no more.

At the last thousand years of the Third Age, the elves of Lorien that in Middle-Earth live with a lord and a lady that are very similar to Thingol and Melian, and with a ring that revives the beauty in Middle-Earth of ancient times.

And I say: Lorien in Middle-Earth at the end of the Third Age mirrors the one in Valinor:

The great similarity of Celeborn to Thingol and of Galadriel to Melian, and the non-passing of time, are actually signs of a mourning over the past and the inability to let it go.

The elves of Lorien are Sindar that are forever grieving the old gone days of their grandparents under the mighty king Thingol. Melian's grieving is echoed by them.

That's actually what the White Ring of Water Nenya is:

A ring of mourning. Mourning over the past, that since the end of the First Age is represented by Melian who grieves in Valinor.

While Elrond's Blue Ring of Air Vilya is a ring of remembering the past in order to learn from it for the present, and Gandalf's Red Ring of Fire Narya is a ring of inspiration and hope for the future.

Moreover, Melian was the maia of grieving already in Middle-Earth:

Her girdle about Doriath at the First Age of the Sun is typically considered by Tolkien's fandom a girdle of military strength. But in spite of it, Thingol employed Beleg and another elves under him as his march wardens. Moreover, if you ask some Noldorin princes - Maedhros and Turgon, for example - they'd probably say it's their own kingdoms who protect Doriath from Angband. Eol's forest, for example, was outside of Melian's girdle and yet wasn't conquered by Morgoth's orcs, and Eol and his servants even lived there pretty well. Eol's forest actually somewhat reminds me of Mirkwood at the days of Sauron at the Third Age, that wasn't inside the scope of Galadriel's ring: both are sunless.

No, what Melian's girdle actually did was to keep the simple, natural beauty of Beleriand that was before the coming of Morgoth and his orcs, and before the coming of the Noldor who loved to build too much and did not live in such harmony with nature as the Teleri loved.

The beauty of Arda that under the stars, before the coming of the Sun.

Both Melian's girdle and Galadriel's ring may in-story have also military-strength (it is said Galadriel protected Lorien with her ring at the War of the Ring) but mythologically, that's not what they represent.

They represent the mourning over the beautiful past that is no more.

Moreover, I argue Melian was the maia of grieving already before the rising of the sun:

She put young Elwe to sleep and so prevented a lot of Telei from leaving to Aman in order to establish in Middle-Earth a kingdom that will keep the beauty that was in all of it at the Spring of Arda, under the Lamps of Varda at an everlasting day, before the returning of Melkor from the Outer Space. It is told at the Quenta Silmarillion that at the Ages of the Trees the sleep of Yavanna that was in Middle-Earth until the rise of the sun was absent from Beleriand because of the power of Melian.

At the Ages of the Trees Melian represented the grieving of Yavanna over the end of the Spring of Arda. Therefore at the Quenta Silmarillion it is told Melian was a relative of Yavanna.

It's going like that:

The Spring of Arda that under the Lamps of Varda at an everlasting day has ended. Middle-Earth is now forever Melkorish. Yavanna, the all-loving Valie, now mourns. After the elves awake Melian, who represents Yavanna's grief, establishes Beleriand, a kingdom, and keeps in it the pureness of the Spring of Arda. After some ages Morgoth comes from Valinor, and Beleriand is now Morgothish. So Thingol takes a small part of it, Doriath, and that part is now kept by Melian at the pureness of Beleriand at the Ages of the Trees. Melian's girdle represents now the grief over the end of the Ages of the Trees and the whole beautiful Beleriand that under Thingol's rule back then. But eventually Doriath is ruined. Galadriel was Melian's student in Doriath, and her ring of power represents the grieving over the beauty of Doriath that is no more. Under Galadriel, the kingdoms of the Teleri that under her husband Celeborn keep the pureness and beauty of Doriath in them. That's to say, keep the beauty that was in all of Arda at the Ancient Spring, under the lamps of Varda in an everlasting day. But after the War of the Ring, Galadriel's ring is no more. Galadriel, Celeborn and all their subjects gradually leave Middle-Earth.

And how does the whole Tolkien's legendarium end?

With Arwen.

Like Melian when she lost her husband ages before, Arwen, now a widow queen too, comes to mourn in a place called Lorien over her losses.

At her death, a year afterwards, there remains in Middle-Earth nothing from the grief over the Spring of Arda that under the Lamps of Varda at an everlasting day. No more earthy kingdom - however small - that will retain the pureness of the non-Melkorish world.