The slots in this component would normally be cut using a rotating cutter, but in this case it would (in theory) be possible to cut them using a fixed cutter (as in a slotting head or a shaper).
The key thing is to be able to index the work piece.
a) Indexable headstock
Some (hobby use) manual lathes have basic indexing features in the headstock - i.e. a ring of say 32 holes in the chuck backplate and a plunger to locate the stationary spindle. Others, such as the Myford which is very common in home workshops, have indexing attachments that can be bought or made like
this one.
With either, the work is held in the (non-rotating) chuck as normal and the cutting tool (either rotating, powered by an auxiliary drive) or fixed in the tool post moved around the work. None of these will work with a CNC headstock though, I don't think.
b) Indexable workholder
Without that feature, the only other option is to use an indexing head (a '4th axis' in milling terms). The 'home shop' solution is to mount one of
these on the lathe cross-slide and hold the rotating cutter in the chuck.
I guess that standard CNC lathe control software only does 2 axes, so you'd need a manual indexer and lots of interupts in the program.
Hope all that makes sense.
For a 1-off job though, it might be easier to find a mate with a CNC mill and 4th axis though!
Andy