For a lathe, you need an active and precise system. I would say max.speeds of 2-5 mtr a minute, although I found anything above 2mtr/min scary. It's different then milling, because everything what goes wrong hits the chuck with a big boom!
You need good acceleration and power for threading to synchronize chuck and tool. I'd say, go for servo's and look for the UHU do it yourself drives. They are discussed here on the forum. For mounting the drive on the Y axle: on your photo#3 it may come into conflict with your family production tools. Maybe you can find a place on the backside. Good luck and keep posting pictures. For some reason they like it here.