I had a beta version of Lion on my Macbook for one day before re-installing Snow Leopard. I accessed my Time Machine backup in Lion and was asked to set it up for backups on this new computer. I made the mistake of saying to do this, but changed my mind and canceled about 10 seconds later. Evidently enough was done in that ten seconds to cause problems. Now when I try to use in in Snow Leopard I am told that the drive is set up for a computer running 10.7 or higher while I'm at 10.6.7 so I can't access any of the files. Is there any way to fix this short of reinstalling Lion?
Unfortunately, you can't. Apple really implemented changes to all aspects of Lion including Time Machine. When you allocated the old SL time machine backup for Lion's use, it modified it for use with Lion's system files. This added support for new features like 'Local Snapshots' which is also part of the new 'Versions' feature in Lion. I'm afraid that backup will only be good for Lion from now on.