Well, the Lynch ESP signature model is maple, according to Sweetwater:
http://www.sweetwater.com/store/detail/EGLK1?adpos=1o2&creative=55280653081&device=c&matchtype=&network=g&gclid=CMSRurm5xMQCFcSCfgodMC0Apw
As such, if you are limiting your choices to the three species you've listed, the heavier, denser choice - walnut - would be where I would go here. With no particular outcome guaranteed, and of course heavily subject to whatever pickup choices you make.
Bagman