You have what is called a Reeve's drive. Very effective speed controls in the entry level lathes, and even some more sophisticated.
First take your wood off, unplug the motor, then put the speed lever (if it wll move) all the way to highest speed setting. Then you should be able to get yer fingers in there and wrassle the belt out. When the belt is free hand turn the pulleys to make sure things are OK. Repower and adjust the speed lever a couple times. This should properly seat the belt and put you back in business. If that doesn't work you will need to dissassemble the unit and reassemble. Reassembly requires some very strong thumb work to compress the spring and get the retainer washer back on. You might need third or fourth hands to help with this. Start with a cold beer and be patient, it can be done.
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