There are plenty people who've successfully threaded with Mach and a parallel port. IIRC there was an issue with the parallel port on it not being able to handle the spindle speeding up during a threading move, but Art fixed it once somebody could consistently reproduce the problem.

Have you ran through the Mach threading guide? It's buried somewhere on the Mach forum.
It's a long time since I've used Mach3 on the lathe, so I'd say you're far more likely to get help on the Mach forum, but make sure you mention you're using a parallel port, and post your configuration XML so people can check your settings.