I just love watching electrical threads on this forum.
Listen to 404nouser, he sounds like he actually knows his stuff. The capacitors have nothing to do with supplying LRA, nor do you even care what LRA is, it's a mostly-useless number for the end user.
A single-phase motor is like a bicycle with one pedal. As 404nouser already implied, the capacitor provides some phase shift to the current applied to a secondary winding, temporarily adding that all-necessary second pedal to get the first off bottom-dead center. Once rotating, it can be switched out, as is the norm on most inexpensive "capacitor start induction run" motors. You can ride a bicycle with one pedal, as momentum carries it past the bottom-dead center "stall point", it's only starting them without a second pedal that's a real problem.
All intersting, but none of this has anything to do with your original question of running the compressor off a generator. Your biggest problem with this motor is that it's only a 120V single-voltage motor, with no option to reconfigure for 240V. Attaching this load to any split-phase 240V generator is going to load one leg very heavily, which will cause neutral to "float" in that direction, and cause output voltage on that leg to drop accordingly. This is not good.