Are you trying to install LW using it's offline installer? That's the best one to use,
not the online (recommended) one.
Try this:
Download the latest Java JRE using the offline installer, see point 1 in the thread below. Remove your current Java version before you install the new one.
Fixes for LimeWire
Now download & install LW, make sure to use the offline installer.
Otherwise, try deleting LW's preferences folder. That's points 2 & 3 in the fixes thread.