OK, I've learned a little more. Thanks to Dave, I found out that the lead screw handle on the apron controls the forward/reverse of the spindle and lead screw (there is a reverse knob also that only reverses the lead screw it appears).
If I try to start the lathe with the handle in neutral the spindle turns for about 3 seconds and shuts down. Is this normal?
I can then lift the handle to reverse the spindle, and everything runs fine, back to neutral no problems, emergency stop but not problems shutting down.
If I lower the handle from neutral to forward after the spindle has stopped it runs in the forward direction. If I switch to neutral it continues to run. If I hit the emergency stop button it continues to run. At first I thought the contacts were stuck on the relay. Then I realized that after a while whether it was running or unplugged that the relay would release itself. The only thing I can figure is it is somehow "bleeding" voltage back off of the start capacitor on the motor or somewhere else. It does it every time, the longer I run it in forward the longer it takes for the relay to drop out, but it does reach a maximum time. The only way to stop it is to unplug it. NOT A SAFE CONDITION!
I need to find where the voltage is bleeding back from.