Because of the very limited amount of room, it’s impossible to use a glass scale on the cross slide of a mini lathe, it has to be magnetic, though you could probably use one for the Z axis i.e. lengthwise.
Although a DRO for milling machines is a no-brainer, for lathes, their usefulness is a bit more questionable – I find it handy, but it’s by no means essential.
The basic magnetic DROs like the Warco one don’t have all the bells and whistles that the set ups like the Amazon ones you link to have, and they are a bit less accurate. You can get high quality magnetic scales which are accurate, and will work with the fancy displays, but they are pretty expensive. I’m not sure I’d want to spend that much on a lathe installation.
If you want to go with one like the Warco, I have a display and a pair of read heads which I don’t need, and I’d sell them for not very much – you’d need to get some magnetic scale strip from Warco (the standard type you can get from AliExpress, etc., won’t work with this kind of display), and make up the necessary brackets, etc.
If you’re interested, PM me,
Andy