There are no manufacturers of screw cutting lathes (a variant of engine lathes and what most people think of as a manual lathe) left in the USA. If you look at old 60s/70s catalogs of lathes the basic models would cost around $15,000 in adjusted money. The Chinese imports are $3000.
Could someone make a competitive lathe for around $3000 in the USA? Perhaps. But it will take significant investment to make that happen. I'm not sure where that investment will come from as Wall Street has no interest in such things.