I have an XSY AT1 1.5kw. I bought as a spare for my Boxford, fitted it to test and it's still on.
Manual is in Chinglish, but as it cost less than £40 on offer and does everything I want I'm well pleased! I use it more as a phase convertor and change gears for speed to keep the torque.
I expect you will need a bigger one for you lathe, certainly worth looking at.