Welding often deform metal. I would use other devices other than a lathe to hold them. Often, the deformity will needs to be factored in before welding so some machining can be done later to correct it.
For example, a tube/cylinder can be used to hold two round stick to make sure they line up to 1 thou. Then through holes on the tube, weld those around the connections. Then cut out the cylinder, weld the rest, then machine it, leave some margin for later cutting. Then straighten the rod using an indicator and a press, then make a final cut.
Maybe there are better methods. If you have one, please share.