The lathe may have been operated when there was no oil in the resevoir.
That will damage the seals for sure. The next time you put oil in it
some of it will leak out through the seals and ya just gotta replace
them eventually. Usually you will notice it if its coming out of the
seals. Oil on the drive belt will make it spongy and soft as well as
make it slip under a heavy load. Oil on the outboard side will just
coat your gears. But you should see it somewhere. Unless you have a
void in the casting that is eating it. I have seen that. Couldn't see
the porosity in the bearing seat (headstock end in this case) but a
liberal dopping of blue ATV before reassembly seemed to make it stop
loosing oil. We did find oil inside the head stock resting on the chip
pan. Didn't find any stream down to that point... I hope you don't have
to go to that extent as the link belts are so much easier to deal with
your other problem.
Good luck,
Doug