Although I'm more of a tool / machine maker than a model maker, I wouldn't dream of attempting to design a lathe myself when there are so many excellent industrial products out there already, available for less than it would cost to make one. Like most MEs, I have only a very superficial understanding of any of the design considerations and decades (centuries almost) of experience.
Even then, I would struggle to design something that I couldn't realistically expect to see made either – and I'm not vain enough to believe anybody would do so. Most machine tools rely on heavy cast iron to provide the basic rigidity and core framework – this isn't something any of us could sensibly attempt, even if we understood how to design it. I suspect you'd have a very short list of entries….
Call me a coward but I'm happy to have a bun fight and vote for a favourite lathe, though!
Murray