My LT 1045 (Kohler SV600 engine) was running fine when I almost ran it out of gas. I added gas but it started running with a miss so I changed the fuel filter. Got it running again and it ran fine (even at high rpm) -- miss was gone. Then I tried to use it the next day and it only turned over to a certain point and would stop (kind of like if the battery was dead). If I manually move the engine past this point (I think it is at the top of the compression stroke) it will turn over again but only to the same point. If I remove the spark plug, it turns over fine. It even started again once after I put the plug back in but, once I shut it off and put the shroud back on the flywheel, it went back to where it would only crank to the same point and then stop. I have a new battery in the mower (300CCA).
Replace & gap new OEM plugs for your engine. Check all ground cables by hand trying to move them starting with battery, making sure no corrosion & cables are tight & secure.
My guess is that you need to adjust your valves the compression release that’s on the exhaust valve is probably not engaging and it won’t let it crank over all the way easy fix