I can tell you something about Bejeweled 3 - as I started playing that with 10.6, and continue to play with 10.7
I was bewildered at first, because it changed the location for the support files, from the main Library, to my user Library folder, with no other change, except for the upgrade from Snow Leopard to Lion. I have not seen ANY other app need to be reset in that same way. The license for that game had to be re-entered. I'll pin that little issue on the game itself, but it works fine once I got that sorted. I know that Bejeweled recommends installation in the main Applications folder, and not in a user folder. That may have helped me, too - thanks for prodding me to look at the developer's site.
The other game you mentioned is a Java game, which would have its own issues with Java versions, etc.
Now that those games are working - are you having other problems?
Just as a hint - try to avoid messing with permissions in OS X, unless it's for some specific issue, and you know exactly how to proceed. Lion seems to have changed how the system deals with permissions, and in my experience, seems to be a good change. It's still a bad idea to try to out-think your OS X system. My experience is that it takes care of itself fairly well.
There's plenty of info by now at various sites about compatibility issues with Lion. Some are simple, others may need to wait for system updates. The issues that I have had mostly settled down to "not much to talk about" after using Lion for a few weeks, except to mention that I have found Lion to be significantly faster than previous version of OS X (if you give it enough RAM), and in my experience, very solid and stable.
I don't use Mac Mail for a variety of reasons, none of them are about compatibility. I haven't tried the Lion version of Mail, and prefer Thunderbird.
After thinking for a while, I think my worst experience with an Apple update was one that ended up formatting the hard drive without my knowledge (and in my dumb days before I started backing up the hard drive). I think it was going from OS 8.0 to 8.1!
None of these little details that I occasionally deal with in OS X are even close to that debacle...