Do you have an assistant?
Have an assistant sit in the seat.
Raise the hood and put your volt meter on the battery. What is your voltage? I want to see 12.4 to 12.9 volts with the key off. Now, tell your assistant to turn the key to start. Read the voltage while they're holding the key to the start position. If it's below 10v, your battery is failing. If it's staying about 12.4-12.8v, the battery is "probably" ok and your issue lies elsewhere-perhaps a failing our misadjusted hst switch, and this does happen from time to time. Sometimes I've seen them get sticks and whatever else jammed into the switch area damaging the wiring and or the switch, but that's kinda odd. Start with the easy stuff first. Battery.
BTW you can test all your safety switches on all of the L-01 and L-02 series tractors. Sitting in the seat, key OFF, hold down both of the yellow buttons in the dash for a few seconds, then turn the key on. In the dash, where your hourmeter normally is (digital), it should say "a". If so, let off of the buttons, then push them down again and hold them til you get a beep. Once you get a beep you can let off of the buttons. Just takes a couple seconds. Now you can work all your safety switch controls and each time you work them you should get a beep. Moving the hst pedal forward from neutral it should beep, and then as it returns back to neutral you should get a beep. If not, the switch is not adjusted properly or the switch is failing or the wiring is damaged. Also check your pto lever as many of them won't automaticlly return to neutral on their own so you have to manually pull the lever back as far as it'll go in it's slot.