Does the rest of the BAU know about Reid's KISS with Lila?

Not unless he told them. They were photographed but morgan and Elle destroyed the film, and no one else saw them in the pool. I don't actually remember if Reid told morgan about it on screen oder not but that's the only way anyone might've found out. Personally I believe Morgan's the only person Reid could've told this, and it wouldn't go any further than him anyway.

To my knowledge, only Derek knows, because Spencer told him at the end of the episode. It is not made known whether he mentioned it to any of the other teammates.

Derek is the member of the team to know. Reid actually tells Derek a lot of personal information throughout the series. ( The KISS between Lila and Reid was Mathew Gray Gublers first on screen KISS )

Yes. morgan knows. Because Du know how at the end he was explaining to morgan about what he was telling her. Ya I don't remember what he said.

OH they know Gidieon saw it happen and blabbed to Hotch but thank goodness REID didnt get in trouble because Lila made the Bewegen not REID

elle actually saw it happening and i think the team had a good idea that *something* a bit personal went on betwween the two of them anyway invovling a pool :)

no only Elle and Morgon knows

Yes, I think so...especially Hotch, he was at the scene in the end...