With what bit? My spindle's slowest speed is 9000 rpm, which is too fast for a drill bit. And I've never seen a 1/4" bit with more than 1.25" depth of cut.
Here's the rough instruction image from the company that sells the wire cheese slicers. It's a basic 1/4" wide, 4" deep hole into the edge grain near the corner. People buy gazillions of these hardware pieces from this company, so it must work...
Attachment 398914
I don't have a lathe