Hmmm...
#1 Your title didn't say live tool lathe.
#2 I was asking of what brands you're already looking at.
Taiwan is the biggest MTB in the world - there's small factories making to print (using a generic design house to design the machines) and then there's companies like Fair Friend Group who are massive and do the lot themselves.
Then there's small swiss style machines with 10mm bar capacity with driven tools, or there's machines with 100mm bore headstock with driven tools.
But sorry, yes, your thread title was clear