Hi Brian,
I agree with Gerald, it is completely feasible to build a model steam engine on a small lathe. Small engineering quality lathes are capable of producing work to extremely fine limits. Many years ago I saw the late Jim King demonstrating at the MEE, making, if I remember rightly, a Stuart 10 engine on a small Cowel lathe.
The real limiting factor is the size of the engine you wish to make; that is, will the largest parts fit onto the lathe. If you consider engines the size Peter Arnots’ V2 or V4 oscilating engines, you should have no problems on a 210mm between centres lathe.
Regards
Mike