I would do this with my hand shaper, which is very useful for small jobs like this. However, assuming you do not have a hand shaper, you can do this in the lathe with a bit of effort.
Centre the work in a 4-Jaw and drill/ream your 7mm hole.
Make a holder to grip the end of a small (1.5mm) parting tool horizontally/flat and on centre. My small ones are 1.5mm x about 8mm I think, so they would need reducing slightly in depth for about 12-14mm (to fit your hole). Grind some relief on the front cutting edge. If I’m not beiing clear, the tool holder doesn’t enter the hole, just 12mm of the cutting tool. It works if everything is set correctly…
You can then slot the work using the lathe rack to work to and fro, putting small cuts on using the cross-slide until you reach depth. Then index the chuck around 180 to do the other slot. There are ways to do this simply with the chuck jaws…
So it will take some time to make the holder/tool and set it up but the actual work will take just a few minutes…
Hope this helps.
Regards,
IanT