First, best to determine if you have an ignition problem or a fuel delivery problem:
do your normal pre-start stuff - good batt, fresh set of plugs,crankcase oil level, fresh fuel, pto switch off, clutch pedal fully depressed, throttle set to mid position (not choked)... Have an assistant remove air cleaner from engine carb and spray several shots of rattlecan carb cleaner directly down throat of carb as you crank engine while sitting in seat.
If engine pops and tries to start, you have a fuel delivery problem. If no effort by engine to try to start, you have an ignition/timing problem.
Fuel Delivery: turn ignition switch on and off several times. Coming from the bottom of the carb, you should hear a sharp click of a solenoid engaging each time you tun the ignition switch to run. If not, carefully remove the solenoid and lead wire and chk the solenoid plunger for being gummed up or stuck. Repair or replace as needed. Let all old gas and any crud drain completely out of carb bottom.
Next, pull leads off spark plugs. Detach fuel line going into carb and using a catch container, crank engine starter and observe fuel pump output - s/b a good stream of supplied fuel. If not, troublershoot backwards to fuel tank including fuel pump and fuel fulter. Only replace any items with OEM parts Kohler engines are very picky about such.
Replace any cracked/damaged rubber fuel lines. Check fuel tank cap vent to not be blocked.
If fuel feed OK to carb, but not to engine, pull and disasm carb. TAKE PLENTY OF BEFORE?AFTER PIX?NOTES TO GET ALL BACK TOGETHER CORRECTLY!! Obtain rebuild for carb soak all part in carb cleaner overnite. Use fine brass wire and magnifier to probe all passageways and blow out with compressed air till dry and totally clean. rebuild carb using kit parts as directed. always use fresh gaskets. Work clean as possible.
Ignition: go to small engine store - invest in an inline spark tester that connect between plug wires and plug to determine presence of spark. Chk for accumulated crap in cooling fins of engine and possible damage to ignition kill wire (entails removing engine cooling shrouds).
If still no start, chk for partially sheared flywheel key. Will prolly require air wrench to loosen retaining bolt and be careful not to break flywheel fins during removal. Gently tap out out key from crankshaft slot. If shearing indicated, replace with OEM key, not aftermaket or generic. have all surfaces clean/dry when re-asm.
For all of above wise to go to Kohler engine website, download both parts list and service manual for your particular engine - get the model/type # off the engine's decal first. Good luck
One caveat: If you've been regularly been using a garden hose or a power washer to soak/rinse the machine down for clean/shine purposes, all bets on above are off. L&G powered eqpt ain't designed/built to withstand a "car wash" treatment - their electrical systems will corrode in ways you don't want to imagine causing gremlins of the highest order.