no, the invalid operation will not be thrown if you call it from another thread in LWJGL; if you do call GL commands from another thread you will get a LWJGLException about contexts...
invalid operation is an OpenGL specific exception, nothing to do with threads..
I've encountered this type of problem with Xith3D's LWJGL renderer long ago. I've filled a bug report for it, it has to do with the fact that Xith3D never checks the hardware capabilities ; it takes for granted a set of capabilities and if it doesn't fit, it will just run as is with OpenGL firing errors. The bug exists as well with the JOGL renderer, it is just not catched. As far as I can tell, this type of bug rely on the Xith3D side, not LWJGL.
OK gonna debug that.
You should use GLIntercept to catch the offending openGL call. It is of great help
Unfortunately, alas, alas it's windows-only !! If you have a manner to make it works on linux (I think Wine isn't of great help here) please tell me.