The usual replacement or source of 5 speed transaxles is the Renault NG3, though jbcollier uses a 395, I believe. Hopefully, he will chime in as I know even less about it than other trannies.
First, I would say that parts for the 365 are more available than I once thought. If you're interested in repairing your 365, you should look into
http://www.mecaparts.com/ and
http://www.alpine-america.qc.ca/. That may be a bit redundant as I am led to understand that Alpine-America sells the Meca line. I mention Apline-America because they claim particular knowledge of Lotus and might have other suppliers that would be helpful.
I know a little about NG3 transplants. The NG3 came from the Renault Fuego which was imported back in the '80s. You may still be able to find one in a junque yard. You can try car-part.com. You would obviously want one from the latest Turbo Fuego you can find. There are modifications to the tranny that are required and are spelled out here (
http://www.greytower.com/jon/lotus/europa/gearbox/gearbox.html). You will also need an alternate shift mechanism. Richard at Banks will sell you the whole shoot'n match (or at least enough to get you close). I believe there are plans on the lotuseuropa yahoo group (
https://groups.yahoo.com/neo/groups/lotuseuropa/info) for cable shifters. When I installed mine, I had to have a new rear hoop installed to accommodate it. That wasn't a huge deal since I was doing a ground up rebuild and I had a friend who was a good welder. I think I have seen where someone was able to use the standard 365 rear hoop but I didn't see how that would work when I did mine. Richard could advise you there.
I didn't mention the 352 since it is a 4 speed but it should be a drop in replacement for a 365 and if you drive primarily in town, you probably wouldn't loose much. I don't know anything about the availability for 352s.