The design use to be on www.makeprojects.com concretelathe Which is founded on lathes built during WWI when cast iron was not available. Machinery June 1916 page 877 - 879. Patent 1154155 Yoemans, the stiffness of the design is lowered since the concrete is at the ends supporting the ways which are pipe.Build it using concrete.
Rediscover Lost Knowledge – The Concrete Lathe
I suggest looking at the lathes others have built. https://www.vintageprojects.com/lathe-milling-plans.html
The Turret and Hobby lathe are good choices for starting point. Another site with a concrete Milling machine on the list is: