The Magnetos can and do fail on Lawnboy mowers. I have replaced mine with both Lawnboy stock Magnetos and aftermarket inexpensive mags from Amazon. The aftermarket are not supposed to be as good, but my experience is they last just as long and the spark is fine. If properly gapping the mag to the flywheel does now cure the issue, then you may want to consider a new magneto.
There are other things that can cause starting and running issues with a Lawnboy other than the magneto and it is somewhat tricky to identify what the issue truly is if you are inexperienced, but, the only way to gain that experience is to try. Carb issues, fuel issues, improper mixture, clogged exhaust ports, air filter clogs, choke issues, bad spark plug, improperly gapped spark plug, reed valve issues and a partially clogged muffler, just to name the most common, can all cause you some gried in starting and running properly on a 2 stroke.
Lots of good info on Youtube. Good luck with the mower. Hope you got it going.