Thunderstorms during this period are typically caused by monsoon conditions, which can affect the entire southwest. Arizona has paid more attention to them because they are particularly impacted, and they refer to
the Arizona Monsoon. Further explanation is given by
NOAA, and they write about the season beginning around the first of July and extending into September.
Bell-shaped curves being what they are, early July and September would see less-frequent conditions than the middle of the season. My personal rule of thumb is to consider thunderstorms a factor in my planning only between mid-July and the last week in August. Again thinking of the bell curve, you might consider the first week of August being "prime time."
By the way, in all my July and August climbs of Mt. Whitney, I made the summit in all but three attempts. Only one, in August, was due to storm. Part of it is knowing enough about the conditions to discern between "looking scary" and "being scary." Also timing it to be heading down in the very early afternoon. From my logbooks, I have gone to Mt. Whitney:
27 times in June. 24 were in good weather, and 3 in poor.
26 times in July. 21 were in good weather, and 5 in poor.
24 times in August. 22 were in good weather, and 2 in poor.
25 times in September. 22 were in good weather, and 3 in poor.
I made several other ascents in the area during these months, for example of Russell, Thor, and Candlelight, with generally the same results.
Of course, thunderstorms can be caused by conditions other than monsoon, and can come anytime.