Yep, as people have said, there has been a lot of very, very fine work done on a lathe using vertical slide attachments (AKA milling attachment).
Certainly over here in the UK in the 50's, 60's, 70's and 80's, the Myford vertical slide attachment would have been considered part of a reasonably well equipped workshop that had a Myford ML7 or Super 7 in it. Same would probably have been true for the Boxford milling attachment in a Boxford lathe equipped workshop.
That said, even with those lathes (which are considerably more rigid than say, a Chinese mini lathe), the moment a model engineer could get their hands on a dedicated mill (the Dore-Westbury was one of the first small benchtop mills available in the UK) or at least a milling head (the Amolco milling head was popular), they'd jump at the chance.
There are things one can do to improve the rigidity of the Chinese mini lathes, which will make a vertical slide attachment more useful, but there limits to the improvements you can make.
Generally speaking, if you can fit a milling machine (even a small Chinese benchtop one) into your shop, and can afford the purchase, your milling capabilities will be orders of magnitude greater, than with a vertical slide attachment for your lathe.