Which version of the Lisa interface are you referring?
The credit for the mouse is generally given to Douglas Englebart, not PARC.
I stand corrected.
The original Lisa OS, which ran amazing applications like LisaProject. I still have the brochures for all of that stuff somewhere around here. Later, Apple distributed a Mac compatibility environment that allow Lisa to run Mac software.
Besides Xerox, another influence was the Corvus Concept computer. Also, Ted Nelson's book "Computer Lib/Dream Machines" was an important source of inspiration for the development of Lisa and Mac.
The Lisa had several design flaws. The worst one, in my opinion: Unlike the Mac, the Lisa's pixels were stretched horizontally, so the aspect ratio was messed up.
Here are some screen shots of the Xerox Alto and the Lisa -
http://www.digibarn.com/collections/software/alto/index.html
http://www.digibarn.com/collections/software/lisa/index.html