I'm having a similar problem. I've had lime wire before and thought I was knowledgable, but this is a totally weird problem. I had to re-install it after my OS went down.
So, I installed, and began to download all the songs I previously had. After they were complete, I cleared the inactive and went into the library to listen. They weren't there. I switched from shared to incomplete and a few were in there (but wouldn't launch). I don't know why. They were complete when I cleared them, and I thought they wouldn't clear unless they were complete, anyway.
After that I downloaded them, again. (Got the same message as the user above... "would you like to write over...?" Yet they weren't in the library.)
But, this time, I didn't clear them when they were complete. Instead, I tried to launch them from the search page and they wouldn't do that, either. So, I cleared tham, again, and went to look for them in the library. They weren't there. I clicked refresh. Still nothing.

I don't have a "saved files" section in my library, as you suggested to the other user. Any suggestions?