I routinely drill stainless, I work in an food production environment. Everything is stainless sheet.
Twist drills in sheet metal tend to make out of round holes. If you must use a twist drill, use Norseman/CTD drills. Their high molybdenum content makes them well suited for SS. Otherwise a good cobalt drill. Lots of feed pressure, low SFM. Use machinery's handbook for the formula for RPM to get the right SFM for your size.
However, if you need a nice round hole, Hougen makes a set of mini rotobroaches. They work excellent, just center punch and drill.
Best lube I've found is Union Butterfield, followed by Tap Magic. Avoid the dark sulphur oil on SS.