Inyo NF has posted an update today on their Mt Whitney Lottery page

4,302 applications entered as of Feb 11

There is a MS Word doc ( Lottery Progress ) showing the number of people requested for each date. This will give you an idea of which days are most heavily requested.

From the summary data in that doc:
 Lottery Progress Report

As of February 3, 2014 2,091 applications submitted.

10 Most Popular First Choice Dates Number of people
Entry Date Combined Day Use Overnight
Friday, August 01, 2014 334 84 250
Saturday, August 16, 2014 297 186 111
Friday, July 11, 2014 274 32 242
Saturday, July 26, 2014 272 214 58
Saturday, July 19, 2014 237 126 111
Saturday, August 02, 2014 222 25 168
Saturday, August 09, 2014 222 84 250
Saturday, July 12, 2014 213 108 105
Saturday, Sept 06, 2014 212 72 104
Saturday, August 30, 2014 199 60 139
Friday, July 18, 2014 193 25 168