Sounds very much like classic case of one-link in a LAG having bad receiver on one side, although if LACP is configured it should figure this out and shut that link down.
What happens is that sessions that get hashed to the defective [somehow] link don't work, while the one's that get hashed elsewhere work. Even/odd is very common for 2 link LAG. For a LAG it is NOT load-balancing it is load-sharing, so even if you have say 4 links in your LAG, depending upon hash algorthum used, maybe hash is only to 2 links - you should be able to tell by looking at traffic stats on the links. To change this behavior, modify the hash algorthum if possible.
Anyway, IMHO, the easiest way to troubleshoot this is to take the LAG down to one link where all sessions work, then add links, and should be easy to find the bad one and go from there.
Anyway this has been my experience for this situation for last 30+ years, but only 20+ with LAG technology -
Good luck.