Hi Mike
I do and have done often, I have a little genny that pushes out plenty of power for the lathe and never had an issue, ONLY thing I would strongly recommend is getting yourself some clear Perspex (Thickish stuff) to build a screen in front of the Lathe, had one incident were someone tried to point at the blank while I was turning, nearly had his flippin finger chopped off 
I don't have any photos of the set up I have - never thought to take any 
As for issues with power, just make sure your generator is powerful enough for the lathe