Looking for her beloved knight
Elayne loved a certain knight to whom she offered a sleeve to remember her. For some reason she was transformed into an ugly green hag standing on a pedestal in a stone circle in Forest Perilous, and her beloved's skeleton (who perhaps was in a quest to rescue her) was rotting somewhere else in the forest.
After rescuing Gawaine, Arthur entered the stone circle, and the hag requested from him the object of her desire. Arthur had already found the sleeve on a skeleton earlier which he offered.
The sleeve was able to dispel the enchantment and she found again her true form. Joyous, she ran to find her loved one, and her disappointment in finding him dead was guessed by Merlin.
By the time the player reaches the stone circle, apart from the sleeve, he has only the purse, the rose and the lodestone. The hag will accept any of them and will allow the player to pass (only once).
Her reply is different for each: she will accept the lodestone because it's magic, and accept the rose as a gift of love, scolding Arthur for rejecting it.
Behind the scenes
Elaine was the name of Launcelot's mother.
The advanced rot of the knight's skeleton and her not recognized Arthur as a king, suggest that she was transformed very long ago.