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Taking it from the beginning you need CAD, then CAM, then a controller for a CNC machine.
Cad you know about, CAM is a program like Cut3D which turns the drawing into G code which is just a text...

Your average CNC mill cuts what we call 2.5D. It's a bit like 3D except you can't cut below an overhang. If you only need a tiny bed, have you considered CNC'ing your lathe with a vertical slide?
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The smaller 'S' is 2.25mm tall, the pocket is 3.5mm tall and 1mm deep with a 1.5 degree draft angle throughout.

Cut on an ancient Roland CAMM-3, cruelly modified.
You need 4 axes, I only have 3 ...