Neither of you have mentioned which OS you're using (mac/windows.) May I suggest you do these things: close any windows you're not using at that time such as the connections window, etc. Go to Tools>Options>Downlds & tick the option for Auto-clear Completed Dwnlds & press the apply button. (For mac osx that's LW's Prefs>>Downlds.)
Update your Java: http://java.sun.com/j2se/1.5.0/download.jsp (take the JRE) For windows users only.

Delete your old search results if they're older than a few hrs. Hide LW in the Dock for mac or program bar for windows.

In your partiacular scenarios it might be a good idea not to use the LW media player.

Don't resume/find resources for more than a few at most files during one session. Doing to many can use up LW's resources & put great strain on your system's resources. Good luck!