The Elvish name for Lothl�rien was Laurelind�renan but it was made shorter perhaps because the forest was fading and not growing. Meanwhile, the origin of the name 'L�rien' is derived from 'Lothl�rien', which makes it a further derivation of 'Laurelind�renan'.
Interesting tidbit
Following the departure of Galadriel for Valinor at the beginning of the Fourth Age, the Elves of Lothl�rien were ruled by Celeborn alone, who led them across the Anduin to found a new, larger realm, East L�rien, centred around Amon Lanc. By the time of the death of Queen Arwen, Celeborn and Galadriel's granddaughter, Lothl�rien itself was deserted.