Looking at the picture posted by Ron the problem, as has been pointed out, is one of fundamentally poor design. The gear that has broken has a very thin boss which clearly wasn't strong enough. It's not easy to tell but the gears also appear to be 14.5 degrees PA, which is also bad, as the teeth will be thinner, and weaker, at the root.
I'd disagree with SoD on a number of points. There's nothing wrong with cost reduction exercises but they have their limits, and I doubt the factories churning out mini lathes pay much attention. If you're going to provide a weak point you don't do it where you have to dismantle half the machine to get to it. You put in a simple, accessible, shear pin.
The late, great JohnS took the view that one of the big problems with the old Myford company was old fashioned, and expensive, manufacturing techniques, reliant on old school skilled workmen. The odd thing is those techniques are often venerated on this forum, but judging by the response on the has anyone bought a new Myford thread far fewer people are, or were, prepared to pay for them. As for many of the manual industrial lathes of the past, industry has changed and very few are now required. So a shakeout was inevitable.
Andrew