I have a 16" Taiwan made Grizzly from 1986. Had it's brother at work for about 10 years. I am yet to see an Asian lathe that does not leak oil. I had a 14" Jet at work,too. It leaked oil all the time.
The cure might be to remove the lower down levers on the headstock,whose "bosses" are usually round. Remove the handles from them,and turn a circular and round bottom groove on the back sides of these lever bosses and put in an "O" ring. Then,when you put the levers back on the lathe,the O rings will be squeezed snugly against the headstock. I'm not sure if the O rings would eventually lose their "tension" and get flattened out,but it would work for a while.
I did the same thing on my 1964 Hardinge HLVH to stop oil leaking through the carriage handle. There seems to have been no provision in this high class lathe to prevent oil leaking,except for close tolerance in the bushing that the carriage handle's axle goes through. I doubt that the close tolerance ever prevented oil from leaking even when new. I cut a ring for an O ring behind the hand wheel and out stopped the leaking. But,this is a rotating hand wheel,and now I need to tighten it up a bit. The shifting levers on a lathe hardly move at all,compared to an apron hand wheel. Hopefully,the O ring would last longer in that application.