I don't know the answer. Motors usually come with a matched controller and without that the repairer has to understand enough detail to make the match.

The 110V brushed DC motor normally fitted to mini-lathes is fairly easy – relatively simple wiring and lots of suitable controllers are sold on ebay and others if you can't find a direct swap for the machine.

Replacing with a 3-phase motor and VFD is fairly straightforward, otherwise it can get difficult.

A recent question about a Wabeco lathe hasn't had a good answer yet because it's DC motor has field winding inputs and a tachometer output, so both it and the controller are unusual enough to be mysterious.

Some other machines are fitted with 2-speed motors, or two or more 3-phase motors. They're a complication I would rather avoid!

Your Seig motor is brushless, details unknown, so although it may be possible to get it going with a sewing machine controller, I doubt anyone on the forum or in the trade knows for sure what to buy. Might get lucky if someone reads this and has done it already. I don't recall anyone reporting having to repair a Seig brushless lathe yet.

Easier to get a brushless sewing machine motor and controller together as a package, because someone else has already sorted out the details. Buying a package avoids the possibility of accidentally causing the dreaded magic smoke, or hitting a wiring puzzle can't be fixed by hard-thinking. As mistakes are expensive, may be better to bite the bullet and buy a replacement motor of the type that's failed – minimal change fitting and reconnecting, so low risk.

Dave

Reading your posts it seems to me that you have no idea what you are doing, rather than cobble something up just to sell the lathe surely it would be be better to sell the lathe as a non runner and let the new owner sort out a motor themselves