“Beset” is the causative verb for “besit”.  The “be-” prefix is only traced to its general sense of “about”.  I am delighted to realize, however, that if I set something down, I cause it to sit.  This word falls off in use after 1850 (Google Ngram Viewer), but is not yet archaic in the meaning for which Tolkien uses it.

• 16.005 they are not likely to overcome the host that besets you;

“beset, v.” OED Online. Oxford University Press, March 2015. Web. 7 May 2015.