Generally, if one is making something like a lathe, one wants it to use (or to sell), In that case, one wants to get it done and start using it. However, if one has lots of wait time, it could be possible to weld the thing together, wait a considerable time and then mill it or scrape it or whatever one is going to do to keep it straight. As for myself, I would just weld it together not expecting it to be perfect, get it as straight as possible and begin using it, then check it often and adjust or scrape or whatever would be needed.
I certainly would not expect a homemade lathe to be a "Benton" of lathes. Years ago in Yakama, Wa, USA, there was a company making lathes. I never got to see their process but I thimpfk they welded at least some parts together. Which makes me thimpfk maybe one could cast certain parts and add it to welded steel parts. I don't know if that company is still in business, my guess is the Chinese stuff killt them.