This sounds very similar to the problem I had several years ago. (I didn't have low oil problems, just the other stuff). I was mowing and towards the end of the job it starts losing power and missing and dies. Pump the fuel injector primer, starts and a few minutes or less sputters and dies.
My problem was, ( as Bob would say) fuel bugs. Clogged the screen filter in the bottom of the fuel tank and atop the sediment bowl. Cleaned the tank, screens, and fuel filter. Runs like a champ again. Always treat fuel now and haven't had a problem in almost two years.