Pull battery. Take to qualified shop that can perform a LOAD test. Today's small L&G batts are somewhat notorious for marginal life and for one or more cells going south. 3 yrs of service is typical - shorter depending on how machine is stored/maintained.
M/W, disassemble and using sandpaper, clean every electrical connection mating surface in the start circuit to bright metal (don't just give it a quick visual - some corrosion can be colorless). Make sure you include batt ground wire to frame connection, starter solenoid to frame mounting. Re-asm all connections tightly. Also chk for corrosion buildup in copper wire strands back up under insulation of batt cables. Put new/good batt back in machine (watch for - to ground, + to harness.... some new batteries have post positions reversed).
if still poor/no starter rotation, bypass ign switch and start solenoid by jumpering directly to starter post and chassis ground with jumper cables. If improvement is seen, replace solenoid first.
If you have been using the garden hose or a pressure washer to wash/clean machine, lose 'em. L&G tractors are not designed/built to withstand soakings.