A Briggs & Stratton engine doesn't have an "oil pump". It uses a "slinger" that just throws oil all over the place inside the engine crankcase.
Just a wild guess, but I think it would be difficult to navigate one of those beasts on too steep an incline. If it IS too steep I would be more concerned about tipping it over and flooding the air filter and carburetor with oil through the breather tube.
Do NOT tip the mower over on its side toward the AIR CLEANER. ALWAYS tip the mower front end UP or (if necessary) over toward the MUFFLER side.
Tipping it to the air filter side at too steep an angle will cause the oil to run through the breather tube, into the air cleaner housing, flooding the air filter and carburetor with oil. It makes a big mess and the lawnmower will not start until you get it all cleaned up.
Just my lousy two cents.