The palette problem on El Capitan doesn't seem to have anything to do with SIP -- I disabled it (and reconfigured LyX) and the problem remained. This is LyX 2.1.4 (on a Retina machine -- the same LyX on a different Retina machine running OS X 10.10.5 doesn't have this problem). If there was a test version of 2.2 available for OSX, I could try that.
Actually, I can't get any of the Greek symbols by clicking on the palette. -- John Kennan