Why does your riding lawnmower crank but does not start?

you need a new battery

If the engine cranks, then the battery is not the problem. Inspect the spark plug and clean/replace and gap to specs. If the spark plug is okay and has a good "fat" spark, then the problem lies in the fuel system. The fuel filter may be clogged and not allowing the fuel to reach the combustion chamber, or the fuel float may be stuck closed.