I notice on the LimeWire Media Player that the player on the bottom of the application (|<, play, pause, stop,>|) has the buttons to scroll through the different tracks on the playlist, but not the option to be able to skip throughout an individual song.

Is there any way that I can skip through parts of songs using the LimeWire Media Player, or do i have to listen to the whole song over again from the start when i miss that one lyric that i really want to hear that was somewhere in the middle?

You can't do this with the LW player. What you can do is disable it (tools > options > player. Untick 'use LW player', apply) & make something else your default player