To answer your question: the DIY or home wood shop doesn't generally use any sort of bit lubrication or cooling liquid. Maybe some applications would use some sort of wax or teflon coating on the bit, but I wouldn't bother.
Use sharp appropriate bits for the material and adjust speed and feed accordingly. It sounds like you are using a hole saw, which has a few problems:
- They don't clear chips well, clogging the hole and adding to the overall work load
- They often have a greater amount of finer teeth, with little kerf and not much gullet necessary for clearing chips
- The large rotating part that holds the teeth is almost always going to rub against the work no matter what you do, holding all that heat and causing burning
Hole saws are really only appropriate for specific applications.
The typical use is to go slow and straight -- try not to rotate the bit out of round around its axis or you will wallow out the hole and cause more friction. Nice even and straight pressure is best, with plenty of breaks to clear chips. A source of compressed air is handy in this case.
Alternatively, you can get a few Forstner bits that are the right size. Get one with the centre a bit proud so you don't have to drill pilots holes. Again, adjust your speed and feed, and allow the chips to clear. Forstner bits have less trouble with clogging, so you might be able to just blow the chips away as you work with puffs of air.
This is also a place where keeping square and true to the hole is important. Two much pressure to one side is where the friction and burning comes from. A drill press or guide is handy in this case. Though, I've had luck with careful hand placement and a centre spirit bubble attached to the base of the drill, in line with the tool bit.