Wow! 1961 Vacuum tube Lowrey. Sounds like you have a project on your hands. But even working, it is probably not worth more than $50. I don't know if Leslie was making the small built-in tremolo units yet, since this was the very first home organ to get a built-in Leslie. Best bet is to take a peek in the back.
"Does anyone know how to fix this?" Yeah, probably... Depends on how much time and money you want to spend. Your best bet is to get a service manual, if you are technically inclined, and start to test various parts to determine where the fault is. Basic technical troubleshooting.
PLEASE BE CAREFUL - there are LETHAL high voltages inside the cabinet, even when it is off. I cannot stress this too strongly.
You can get a service manual for it from: