That's due to LPE & WS both using the same OSX program reference which is com.limegroup.gnutella
This approach is recommended by Apple. Unfortunately LW clones or variations can get into the mix.
I used to have the same problem when I had an old LW4 clone called MP3 Rocket installed. LimeStart started to open MP3 Rocket instead. This issue is user account specific. LimeStart does not open WireShare for me.
The fix would be to remove WireShare.

LimeStart could instead use the program name, but some people rename program titles or/and move the program's location which would prevent LimeStart from finding the program. Some people might also have multiple versions of LW on their system which adds to that complexity.