Upside down? You mean like drilling over your head?
You can find cutting (or sometimes it'll be tapping fluid or something similar) oil at a decent hardware store but I usually just keep a small bottle of 3-in-1 oil for random holes, putting a drop on every few seconds either on the surface or the end of the bit as I'm drilling or use a spray oil, even penetrating oil or WD40 will work alright. I've also found dipping the end of the bit in a little cup of motor oil worked and even a couple of times using bike chain lube (which is more like a thin wax) even. You might have to get creative, you just need to keep some lubricant between the metal and bit.
Go slow, even pressure, don't push too hard or spin too fast. You want to see chips or spirals of metal coming off. If you don't see cuttings coming off, slow down, maybe a little less pressure but not too light that all you do is burnish the cutting edge of the bit. Wear glasses!