You need to get any traces of water out of the crankcase, and that is a bit of a problem without taking it to pieces. One approach I've seen used in this situation is to shake all the water you can out through the oil filler (by removing the dipstick, picking the mower up, tilting and shaking it), putting a spoonful of oil in through the spark plug hole, filling the sump with clean oil, starting the engine, running it for say 3 to 5 minutes, stopping it, and tipping the oil out of the sump through the oil filler, into a container. Drain it fully again, by tipping and shaking. Look at the oil in the container. If it is a bit milky, that is an emulsion of oil and water. Refil the sump with new clean oil, run it again (you won't need oil in the plug hole this time), and drain it again. Repeat this process until the oil is not milky when you drain it. At that point, you can put that last batch of oil back into the sump and regard it as ready to mow some grass. The milky oil, however, cannot be used in an engine. The sooner you give the mower a good run under load the better: that will help to vaporise the last of the water and get rid of it through the breather system.
The problem you might still have, is rust that has packed in around the piston rings in the ring grooves. If that has happened, you can't fix it without dismantling the engine.
