using Olympus Four Thirds on Panasonic GX-1: compatibility question

No practical experience on my side I'm afraid, however you may want to check the Panasonic page, too:
http://panasonic.jp/support/global/cs/dsc/connect/gx1.html
which doesn't seem to explicitly refer to a given version of that lens.

This is all with the Panasonic adapter though - but there was a recent thread in this forum discussing possible differences between those adapters, which may be of help.