Friends, this is “lie” as in “lie down” because the next line of the song is “There lay they long” and, as we all know, “lay” is the past tense of “lie”.
It’s going to take me the whole weekend, at least, to sort out Lie/Lay/Lie among the words of the Hobbit, so meanwhile for your pleasure, here’s the video on the topic that I made for my wonderful students:
I. 1. a. intransitive. Of persons or animals: To be in a prostrate or recumbent position. Formerly also with reflexive pronoun.“lie, v.1.” OED Online, Oxford University Press, December 2019, http://www.oed.com/view/Entry/108041. Accessed 6 December 2019.