To take the guesswork from the equation, connect the alligator clips of your multimeter to the red wire at the starter and a ground source. If the meter reads about 11-12 volts DC with the key in the start position we can assume the starter should be cranking the engine if all else is normal. So yes, at this point it may be time to pull the starter and inspect the pinion gear.
As always, keep an open mind when troubleshooting lawn tractors. There are very few mowers that are normal and rushing to the parts store is often money not spent wisely.
