Fuel, air, spark. That is as long as you have used the correct oil/gas mixture in the mower and didn't seize the engine.
The ignition module in the Lawn Boy mower is a fairly common failure. I had one fail on mine. There is an improved and upgraded one available now.
If the engine turns over easily and has fuel and a clean air filter then I would suspect the ignition module first. Either visit Lawnboy.com to find the number for your model or just call a Lawn Boy dealer to get the right part.
If you can use a wrench and screwdriver it can be a 'do-it-yourself' repair. The engine cover needs to come off. The module is bolted to the top of the engine by the flywheel and isn't that difficult to replace if you are handy with tools.
Otherwise either pay a dealer to fix it or find some handy person willing to do it in your garage.
The module isn't cheap. Mine cost $60, but they normally last a long time so it will be a one time repair.