Here is a link to a
schematic. They have the OEM motor for $286. Here is a link to
Delta Parts if you want to be official about it. It may be a good idea to get the exact part no. from Delta, and then internet search for best price. The model number I am coming up with 62-239, seems to be obsolete...so there may be a newer part no.
That said, its just a typical 3/4 horse electric motor. If it were me, I would just pull the specs (on a metal plate riveted to the motor) and get the cheapest electric motor (within reason) I could find, and mount it up. Make sure the RPM's match up, and the spindle matches up. The motor has a mounting plate on it that allows it to marry up with the lathe. You should be able to take that mounting place off and bolt it onto any other electric motor.