Attached are wiring diagrams for a JD LT155, one for a 3 amp system (3 position keyswitch) and one for a 20 amp system (4 position keyswitch).
For the 3 amp system the keyswitch positions are: 1) Off, 2) Run, 3) Start/crank. For the 20 amp system the keyswitch positions are: 1) Off, 2) Run w/lights, 3) Run w/o lights, 4) Start/crank. Wiring Diagram JD LT155 with 3 amp system.jpg Wiring diagram- JD LT155 with 20 amp system.png
Do you have power to the keyswitch? If not, there is a fusible link between the battery and the keyswitch. You can blow this fusible link in a heartbeat if power is shorted accidentally. Also check all fuses.
There is a white wire that goes to the ignition module. The white wire needs to be grounded in order to kill spark to the engine. When the key is turned off, the white wire should be grounded, and since it keeps running, obviously the white wire is not grounded when the switch is turned "off".
Your problems could be related to a faulty safety switch. The seat switch is often the culprit....disconnect and use a jumper wire to bypass it and check results.
There are guys on this forum that are much more knowledgeable than me. Hopefully, someone will pick up on this and carry on.