Clickspring has an excellent video on simple shop-made drills:

https://www.youtube.com/watch?v=N1aj_3tlQhU

You don't need the lathe (though he uses one to rotate it for easy sanding, a drill chuck would work just as well), merely a stone, a torch, and some stock of appropriate diameter...you only need the lathe if you're starting with a shapeless chunk, and this isn't the stone age anymore!

https://www.mcmaster.com/metals/hardened-undersized-high-spe...