This music is played during the Fellowship’s departure from Lothlórien in the Special Extended FOTR and in some extra scenes in TT. For fantastic breakdown of the song and its Elvish components, see here. It is a bonus track on the iTunes version of the TT soundtrack.
The day I found this song, however, I had just finished watching TT and was still in the throes of mourning for Haldir and all the Elves at Helm’s Deep (for like the umpteenth time — they shouldn’t have even been there!). I immediately interpreted the title as a reference to the departure of Haldir and his troops from Lórien. It’s Haldir’s first lament, if you will, the lament for all these Elves and their willingness to sacrifice the grace of the Valar for Middle Earth. Saying farewell to Galadriel, knowing they are likely going to their doom, &c. Damn feels.