[Nerwen]

My guess is that the speaker is Thingol, addressing Melian:

Ere the Light came, we were there
Long ago our reign had started
These lands we ruled together
And we believed that our designs couldn't be thwarted -They ruled their realm in Middle-earth before the rising of the Sun and Moon.

Two children we called our own
One of our body, the other in our mind
And though both of them fell down
Only one shall continue our line -The child of the body is Lúthien. The other might be Túrin, whom they fostered.

Here did we dwell
Till greed overtook me
While this is farewell
I pray that we shall meet once more -Thingol's obsession with his Silmaril led to his murder by the Dwarves of Nogrod.