This is a job for an Engineer!……..Only a quality job is good enough for this application!
I`ve made an attachment that fits the lathe toolpost with a hole drilled…….dead on centreline
The material is a 4mm length of solid plastic

Not a bad start?

Using a micro tool, the drill is pushed through the guide hole and the tool slide is set to about 0.5 mm depth of cut.
Cut a groove in the plastic, to test the cutting action
So far so good!
The tricky part now is to sort out the change gears to obtain a 4mm pitch!
If things don`t work out, it ain`t for the want of trying!
Back shortly
Bob