I sometimes chuckle when I read some of the "suggestions" concerning drilling holes in lugs so I thought I would present some of my observations. I have drilled a few and also being a machinist have a little knowledge about such things as drilling holes.
I have read more than once people suggesting to run the drill at slow speed. This is absolutely wrong! If you run the drill too slow, especially with a small drill bit, your chance of snapping a bit skyrocket. When drilling lugs I run the spindle in my mill as fast as I can, which at 2500 RPM is actually still too slow.
Case must be held rigidly. I use a mill but a cheap drill press will likely work in a pinch. A really cheap drill-press may have too much slop in the quill to allow a good precise clean "spot" with the center drill.
Start the hole with a center-drill (#0 for DJ holes or #1 for the bigger ones).
Use a drop or two of oil. This is more for "grab" prevention than cooling. To cool you would need a constant flood of cutting fluid.
Don't feed too slow or too fast. Too fast and you might break a bit and too slow may "work harden" the material you are drilling.
Use a sharp bit. Cobalt bits will last longer/drill more cases but are more expensive. Change bits just as soon as there is even a hint of it starting to dull. Failure to do this might result in a "wallered" hole or broken bit.
If you do happen to break off a drill bit, and can't easily remove it, don't freak out! Don't make matters worse by trying to drill or dig it out. Mix a strong/concentrated citric acid solution and dump the case into it. After a week see if the remains of the bit will crumble, if not put it back in to soak for another week. After a couple of weeks the bit will have rusted enough where it will have pretty much dissolved. Once the remains of the bit are all gone put some oil in the hole and finish drilling. The citric acid will not harm the stainless steel used in our watch cases.