Both my wife and I had a similar problem with our .Mac/MobileMe/Me accounts on our respective computers and iDevices. It started a few days before we upgraded our computers to Lion and continued for another day or two after the upgrade. We did not change anything to do with our accounts and after several rather annoying days the replications of deleted mail went away and it has not recurred since.
My supposition is Apple was getting their new data center on line and they were probably either reloading the IMAP servers or were bringing new IMAP servers on line from backups. I have seen this happen before with other email providers.
Thanks for the help. I thought for sure I was going to have to have a small animal sacrifice to fix the problem.
After about 20 minutes of it reloading 136 emails into my inbox over and over and over and over and over again it seems to have regained its mind.
But for a while there it was making me want to run screaming from my office.