If I was in the market for a lathe that small, I’d probably just buy a slightly larger mill and work on rotating parts vertically, TBH.

If you were committed to wanting a small lathe and CNC, I’d just put linear rails on some of the larger 8020 profiles and rig a spindle from a cartridge spindle. Honestly, though, an 8x16 lathe is kinda bare minimum for steel parts unless you are working VERY slowly. The 7x14 I had worked, but at that scale, I’d be working hard to implement a clough42 ELS conversion so that threading didn’t suck so bad.

If this is genuinely something you want advice/help with, feel free to email me.