Were you ever able to see your shared LW tunes playlist when using 5.2.13 with iTunes 9? Which did you update first - LW or iTunes?

Did you ever use an older version of LW with iTunes 9?

Are your Pro benefits current (ie can you still download a Pro version from your Pro download page whenever you want to)? If your Pro benefits are current & you didn't opt for the 'one off payment' Pro then you could try installing an older Pro to see whether that fixes the issue. But if you don't have current benefits you wouldn't be able to do that & would risk losing your current Pro version, unless you've saved the installer.

There have been some issues between LW & iTunes with earlier versions of iTunes. Hopefully it's not happening again with iTunes 9.

If this has just started happening since installing 5.2.13, you could also try deleting LW's preferences folder when LW's properly closed.
See point 3 here & also point 2 if you've used older versions of LW in the past (there could be a folder in either location).
Fixes for LimeWire
This will change all of your settings within LW's options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.
Vista users: LimeWire Pref Folder in Vista