The problem you're describing sounds like its possibly caused by a corrupted MU. The reason I suspect the MU is that it's likely read or written to 1 last time when you exit to the X360 dashboard. Tomb Raider Legend might have a poorly implemented error routine that results in you being dumped back to the title screen due to an MU read/write error. It will be interesting to see if this still occurs once you get a harddrive.
Hopefully that's it since I probably won't use the MU once I get my hard drive. I'll see if there's anything out there about corrupt MUs.