Michael is right.
I did it once and learned my lesson.
I converted an old Sears Atlas wood lathe to metal and it drove me nuts. Also didn't work as well as the metal lathe I ultimately bought.
First you have to gear it way down. Very small pulley on the motor and a very large one on the lathe. That's easy to say but you can't fit a large enough pulley on the lathe so you have to build a torque box and run the lathe directly from that.
Then you have to but a headstock. That's not cheap. Even a cheap one will run 150.00 or so.
After you fit that, you need to buy a cross slide....a cheap one will cost 65.00 or so. You need the cutter holder, make mods to the tail stock, reinforce the rails so it cuts down on the chatter......etc, etc.
Take my advice. Buy a used lathe at the very least,