OK, so that this thread doesn't become stagnant and fall prey to You-Know-Who, I'll hazard a guess:
The speaker is Laurelin, and her lover Telperion.
Out of time, out of place, - in Aman
Gold my hair and green my face. - gold her fruits and blossoms, green her leaves;
Maiden-like I fenced me in;
He loved me and I loved him. - well, yes... don't know exactly how to make that fit...
Though we quarreled by and by, - they climaxed (er...
) at different times, leading to the mingling of the lights, etc.?
For my sake he left to die. - ???
My guards left me, fair and fresh; - presumably gone to the festival on Taniquetil;
They arrived and fouled my flesh. - Morgoth and Ungolianth.
When at last we met again, - her last fruit and his last blossom, the Sun and Moon?
Both our selves all scarred with pain, - sunspots and moon craters?
To my horror I could see
He no more belonged to me. - their orbits out of sync with each other
He left me under another--
Where shall I find such a lover? - Hmmm...yes, well, where indeed?
Doesn't fit too well, and since you said
Urwen was 'close' with Nimrodel, it's probably far off the mark... I've got another idea, but that needs more thinking.