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If you haven't saved the playlist, simply click on songs & then click on the Remove button.
If you've saved the playlist, click on the Open button & you'll see where you've saved the playlist (if you've kept the default location it will be C:\Program Files\LimeWire for Windows...wouldn't know about other OSs). Navigate to the location & delete from there.

The LW player is not a good one. That's why a lot of people choose to disable it & use another player with more capabilities.