Just to give you an idea, I paid £150 for my Union Graduate bowl lathe, complete with 14" outboard faceplate and sanding table. I have seen these tables sell on ebay for about £70-£80, and faceplates for about £30. I think it was really cheap for a graduate, so I was lucky but nevertheless those are the facts. What I was getting at is it may not be worth throwing good money after bad. If you can get a suitable part easily and cheaply then fine, go for it, but please be aware that what you have is a low quality piece of kit.
I know we can't all afford top quality tools, and I have a couple of Lidl / Aldi tools myself. I bought them knowing they would get only occasional use and it wasn't realistic to buy mid to top quality kit for such use. By the same logic I have some Axminster hobby range machinery. When it comes to a lathe though, I don't think occasional use applies, and I'm sure many turners will use a lathe for several hours at a time. In that situation I wouldn't expect cheap tools to be satisfactory.
I also think many people try to learn woodturning on their own, perhaps with the assistance of a book and I think there are enough difficulties to overcome without having to work with inferior kit and I suspect a cheap lathe is just what you need to put you off turning because you don't realise the problem is the lathe, not you. My B&D attachment very nearly did that to me.
Different topic but same concept - I always thought planing wood was some sort of mysterious black art, until I tried planing with a reasonable hand plane and a sharp blade instead of the blunt block plane I had.
K