I drill on the lathe by putting a dimple in both ends of the blank, holding the blank against the live center in my tailstock, and advancing it into a drill bit held in a Jacobs chuck driven by the headstock. The jacob chuck was $7 at harbor freight. It seems scary until you do it. I hold the blank not by hand but rather with an adjustable wrench. I start the hole by locking the spindle and turning the blank by hand. Works for me, and I cut the blank to length after drilling.