I didn't have a 2" hole cutter but I did have a 1" cutter. I cut three holes in the lid in a triangular pattern. They are 1" in diameter, and three 1" holes should have roughly the same amount of air flow as a 2" hole.
I tried the bike with no lid as well and the intake noise echoes upward and makes the bike extremely noisy when accelerating. If you drill enough holes through the lid it will provide enough air flow in my opinion and is only a little more noisy than it was from the factory.
Also make sure you adjust the screw properly. I had the bike running way too rich when I first took it out, and it would hesitate a bit when I would open up the throttle. I thought it was a problem with the air box being too restricted but it ran smoothly when the screw was adjusted properly. The Kientech instructions say you should tighten the screw 15-16 full turns inward, and back out I think 1+1/8 turns. I ended up backing it out like the instructions said but my bike was running a little lean. I brought it out another full turn and it's running much better now.