Nearly all lightning strikes occur during the months of May through September and about 85% are due to surface heating. Figure 1 shows the cumulative distribution of strikes by month for the years 2000-2012. As you can see, the overwhelming vast majority of strikes occur in the months of June and July.
Figure 1. Cumulative distribution of lightning strikes recorded by BLM in Alaska from 2000 to 2012.
This provides an interesting perspective on the year-to-year variability but doesn't tell us a lot about the spatial variation. Since the BLM data is geocoded, we can place the data on a map. Figures 2 and 3 show all of the lightning strikes from 1986 to 2012 around Anchorage and Fairbanks respectively. Each map is exactly the same scale and represents an area of 1,120 square miles. Most residents of Alaska are not surprised to find out that more lightning occurs in the Interior than the Southern Coast. However, the disparity is fairly striking (pun intended). The Anchorage area receives 1 lightning strike for every 45.0 square mines annually. The Fairbanks area receives 1 lightning strike for every 2.35 square mines annually. That means lighting is approximately 14 time more common around Fairbanks than Anchorage.
Looking at just he Fairbanks area, we see that 50,030 lightning strikes have been observed during the 1986-2012 time period for an area within 50 miles of Fairbanks. Half of those strikes occurred between June 16th and July 12th; a 27-day window! Figure 4 shows the distribution of strikes by 10-day time intervals around Fairbanks.
Figure 4. All lightning strikes within 50 miles of Fairbanks from 1986 to 2012 and a chart showing the frequency of strikes during 10-day intervals.
A look at the observations from the Anchorage and Fairbanks International Airports gives a good impression as the proximity of these storms to the respective airports. During that 27-year time period, there were 26 days with thunderstorms at the Anchorage International Airport and 210 days with thunderstorms at the Fairbanks International Airport. That is an average of 1.0 per year in Anchorage and 7.8 per year in Fairbanks. Since the number of lightning strikes around Fairbanks is 14 times more than around Anchorage, and the number of thunderstorm days per year in Fairbanks is 7.8 times more than around Anchorage, this tells us that any given thunderstorm day in Fairbanks is likely to experience twice as many strikes as a thunderstorm day in Anchorage. One factor not accounted for is cloud-to-cloud lightning. I am not sure if the BLM data captures those events or not. Figure 5 shows the annual number of thunderstorm days at the Anchorage and Fairbanks International Airports.
Figure 5. Number of thunderstorm days per year in Anchorage and Fairbanks (observed at the respective airports) from 1986 to 2012.
There are several papers that provide maps of thunderstorm frequency across the state. One is linked to in the first paragraph on this post. Others can easily be found using popular search engines.