How do I produce the .bbl file required for arXiv using JabRef for bibtex and Lyx?
See the script posted here: http://www.lyx.org/trac/ticket/4624
Note that there are problems when there is more than one bibliography.
There is a script included in LyX 2.1 beta 1. Look in lib/scripts/include_bib.py.
The general idea is that to produce a PDF file, LyX copies your .lyx file and .bib file to a temporary folder, generates the .tex and runs pdflatex (or other) on it and bibtex. Then LyX copies the pdf back to the destination. You need to tell LyX to also copy the bbl, which is in the temporary folder. The way to do this is to create a converter. See Help > Customization for more information.
A quick and dirty way is to view as PDF, then (without closing LyX), find LyX's temporary folder (see Tools > Preferences > Paths for the root location).