I went out to my shop and looked more carefully at the wiring and contrary to what "Busy Bee" said, it can be run as 110 or 220V. I took some pictures of the wiring on the lathe. Maybe this will make more sense to someone else.
I finally had a motor repair person come and work on my lathe wiring. He spent about 45 minutes figuring out the wiring to use. The following picture shows how it should be wired for 220V.
Black to black, white to red, grey to white, and green to ground.