Found this on the
Mount Whitney Lottery - Permit Reservations page:
2015 Lottery Progress Report (as of March 3, 2015) Scroll down on that document, and you can see every date in the lottery!
Generally, for overnights, the top applications are for Friday and Saturday starts in July and August. For day hikes, most are Saturdays in July and August.
Friday, May 1 is an anomaly: While most days in May are never filled, many people seem to put down May 1 as their first choice since it is the first day of the lottery. Just seems odd they would pick such an early date, since they could just walk in and pick up a free permit.