If it is a big hole plug it, if you want to prevent leaks then use Green Slime in all tires, I use it in my mower, wheel barrel, golf cart. This stuff works wonders.
If you lawnmower tires are fillable with air, I have used fixaflat spray available at most harware stores. The type of stuff you use for emergency patching on a car.
The best solution is to install inner tubes. The tubes are available online, or at small engine repair shops. Liquid tire sealants are an easy solution. These liquid sealants do make a mess when you have to change the tire.
You can get a bead sealer from a quality tire shop or automechanic shop. It will probably work best and I would describe it as a liquid rubber that will seal the tires nicely. It is quick drying so no worries there.
