How many times did you try to turn the engine over? Once? Twice? Ten times? That’ll really make a difference in the survivability of the engine in this situation.
Another factor – was there already oil in the pan when you put the gasoline in? There was, right? This is a lawnmower that’s used, as in, this isn’t the first time it’s ever been started, right? I’m assuming there was oil there, but you added gasoline to the oil. What that’s going to do is dilute your oil and really break down the viscosity (the “thickness” of the oil, the quality that makes it a lubricant).
So you’ve got metal parts sliding on metal parts with this thin sheen of oil between them lubricating them – that’s the normal operation of your engine. What you’ve done is taken that thin sheen of oil and thinned it down much, much more. You’re not going to be in too much trouble unless you tried to start it over and over and over. If you did that there’s a possibility you’ve damaged your cylinders and then you’re talking some big bucks for repairs.
However, what I would suspect happened was this – you put the gas in, you tried to start it and nothing happened. You tried again and nothing happened, then you tried a third time and saw the gas coming out the grill in front. Am I right? If so, you’re probably OK.
Remember that gasoline and engine oil are both petroleum products. They’re related but dissimilar in function and form. The good news is that they’re not so dissimilar that simply mixing them is going to destroy the engine (although it’s not doing your gaskets any favors, that’s for sure).
I think – and bear in mind that I’m no mechanic here – I *think* you’re going to get away with the equivalent of a flush job on your oil pan. You’ve essentially flushed it with cleaner and tried to turn the engine over a couple of times. It’s not the best thing to do to the engine but you should be OK.
Take it to the mechanic, he’ll flush it out, refill the oil and it’ll start up.
That’s my prediction.
As long as you didn’t blow any gaskets, that is.