I think M39x4 is very rare, used on big metal turning lathes.
I have found backplates for metalworking chucks at this size but no adapters for wood turning chucks.
My lathe is old, to heavy for me too move alone, it has no visible manufacturer labels.
It may well be a custom build, wide Span and long length
It has a metal turning type 3jaw chuck the previous owner used it for wood. 17in span.
Unfortunately the spindle is indeed threaded at M39, I saw the Sorby M38 but it’s thread at 3mm.
It look like I have a solution with Oneway, they have offered to cut my an M39 adapter for thier stronghold chuck. Hopefully this will work out. It a superb chuck too.