As stated earlier, 2stokes don't care which way the crank rotates, the piston still goes up & down. Intake & exhaust duties are controlled by ports cut into the cylinder which are opened & closed as piston moves up & down.Intake & exhaust "timing" is the same then regardless of which direction the crank rotates.
Two strokes have porting in the cylinders, and a valve which controls intake into the crankcase. IF the 2-stroke has a reed valve, such as the little Cox .049 Thimbledrome, or the large weedwacker type spark ignition engines, they can run backwards.
But most RC model engines the intake is controlled through a rotary valve that is milled into the crankshaft. The only way they will run backwards is if they are flooded, and they will only run until the fuel puddled in the crankcase is expended. While running backwards, they run slow, sputtering and spitting fuel out of the carb, and just for a few seconds until the muffler fills with exhaust... no air, no run.
If the lawnmower is a 2-stroke with reed valve, it will easily run either way.