would a LOx(liquid oxygen) and high octane gasoline mixture increase the energy output of an internal combustion engine? could this be used in a generator to increase its output?

Yes, but remember it also costs energy to create the liquid oxygen. Also, you'd probably need to re-tune the engine to get the greatest benefit. Also, there's other ways of getting oxygen concentrators that will concentrate atmospheric oxygen. These would have the benefit of saving on the constant cost of LOx and the costs and dangers of its storage, but would come at an energy and equipment cost.