You are correct; the proper way to phrase it is Let George and me know.
To understand why you're correct and your colleague is wrong, imagine that we took "George and" out of the sentence. Would you say Let I know? Definitely not! You would say Let me know. So only George and me is correct.
As for why your colleague got it wrong, it's probably because of hypercorrection, which is trying so hard not to make an error that you make a different error instead. ("I vs. me confusion" is #5 on that page!) Children often seem to say "Jenny and me went to the pool", and then they are scolded by adults who tell them "It's Jenny and I", and then they grow up thinking that it should always be "X and I", when the real lesson is about whether the pronoun is in the subject position ("Jenny and I went to the pool") or the object position ("You should come with Jenny and me").