The toe should be off the ground slightly. An old trick by some fitters is to get on a hard flat surface, and then have someone slide a business card under the the club from the toe towards the heel until it touches the sole of the club and stops. The leading edge of the card should be about half way into the club face.
Why is that? Don't people get fitted with a flat board and impact tape to make sure they have the right lie angle?
Seems the toe in the air slightly would go against that strategy.