Sorry, but I'm not sure what you mean.

Do you mean that when you're clicking on the shared 'LimeWire Tunes' playlist (in iTunes) you see the prompt?

Which OS are you using?

Which versions of LW?

Guessing that you're using a later version of LW 5 - within LW go Tools > Options > My Files. Click on the button to configure how files in your LW interact with iTunes. Is the 'Require Password' box ticked??

If you've set things up to require a password, but don't want to use that feature any more - untick the 'require a password' box > ok. Then click ok again on the main options page.