I ran one successfully the other night.
Mac OS 10.9.4, LR 5.6, VGA connect to an old Panasonic projector (haven't got access to model no.). No problems. Our projector doesn't handle 1920 X 1080 though.
Didn't do anything special. Plug it in and pressed play!
Probably no help to you except that the issue is not likely to be Lightroom. Has worked with previous versions of LR and MacOS no problems, too.
Similar to Mac. But projector only 1400x1050.