This is a question based on my experience. I cannot say that lightning (succeed by thunder) never occurs during the day, but it seems most likely to occur during the night. Maybe the humidity levels in air is a reason for thunder and lightning, as they always seem to be followed by rain. But even on rainy days, lightning seems more likely to occur at night. Why it is so?
To add some foundation to the day/night consideration for when lightning is most often seen, here is a plot from Global electric circuit implications of combined aircraft storm electric current measurements and satellite-based diurnal lightning statistics (Mach, Blakeslee, Bateman: 2011)
And to add a better idea of how much regional variability is involved, this plot of peak lightning time from Cloud-to-Ground Lightning in the United States: NLDN Results in the First Decade, 1989–98 (Orville and Huffins: 2001)
The summary is that the majority of places see peaks during the afternoon, but there is variation.
Generally, the mechanism responsible for the majority of storms heavily determines when peak times occur:
- Devoid of other overwhelming factors, the afternoon will generally be favored. This is because that is when peak atmospheric heating occurs. To form a thunderstorm, air must rise until it can attain a level where it has cooled to being saturated. Without external forcing mechanisms, the air rising must start warm and moist enough to reach this point. This instability peaks during the daytime. Nighttime air is indeed typically closer to being saturated (has a higher relative humidity)... but that is caused by the ground cooling. This cooling causes an inversion of warmer air in the profile aloft, which further blocks rising motion. Plus at night there are no longer the thermals created by the ground heating to actually induce the lift.
Many regions have these predominantly airmass thunderstorms, where most storms are found when warm-season airmasses reach their convective temperature during the afternoon (seen in places such as the interior southeast US). For much more details into this lift process and all of these terms, this reference may prove helpful.
- Areas nearer warm coastlines are often heavily biased by the sea breeze circulation. Areas 50-100 miles inland would peak during the early or mid afternoon (see Florida). Spots further inland may actually see a lesser (usually secondary) peak later into the evening because the (less common) deeper penetrations take longer (seen in places like central Georgia). And locales right along the coast may see noctural peaks due to nearshore landbreeze storms (see right on the Gulf and Atlantic coasts).
- Regions dominated by synoptic storm systems may peak during the day if they are where storms typically develop (often along mountain lees). As those storm progress (eastward in the NH mid-latitudes), they often grow upscale into squall lines or MCCs, and in such areas at least secondary peaks may be see later into the evening (occurs in many parts of the Mississippi Valley). And some areas are heavily influenced by overnight low-level jet storm development, and thereby peak during the night (such as the Great Plains).
One last factor that may impact our own experience is the reality that lightning is visually less distinct to us during the daytime. Lightning can regularly be seen for hundreds of miles at night (often given the misnomer heat lightning), whereas during the day, unless the sky is particularly dark or the actual channel is directly observed, often we'll only notice the thunder.
But indeed, while lightning varies greatly geographically, overall it peaks during late afternoon due to the nature of convection, and aided by many of the local mechanisms that drive it.
Day or night are not the correct factors to consider, thunderstorms occur based on instability in the atmosphere when air masses having different properties collide. Look at the NOAA website for more information.
The Stormspotter guide, http://www.nws.noaa.gov/os/brochures/SGJune6-11.pdf, starting at page 15 explains how thunderstorms happen.