Your graph VALIDATES your perception of lightning happening at all times of the day. The graph ALSO shows that average frequency of lightning (well, thunder) is simply HIGHER during the mid-to-late afternoon. If you think that your local observations are contrary to this data, you would first need to diligently and accurately keep observing records. First, track thunder, not lighting. Lightning is perceived more easily at night. That is one key part.
Now, since thunder is produced by lightning, the graph is effectively showing that lightning goes on day and night. Your question implies the graph somehow disagrees with the idea that lightning is occurring throughout the day and night. It does not, it only highlights the frequency changes.
Second, you might have a biased memory. If you want to challenge this data, take accurate observations on your own. You might be surprised that what you thought you were observing was not actually what was happening. :-) Your local storms might not produce as much thunder (and thus lightning) as you think. Consider that massive tropical thunderstorms can produce more lightning than you can imagine, and this can happen day after day in the tropics. In the US, you can also get mesoscale systems that are blasting frequent lighting, but those don't occur as often as you may think. Sure, you might see thunderstorms every night for two weeks at some point in the summer if you live in the Deep South, but you won't see the same frequency of lightning day-after-day that you will see in some tropical storms. Consider that a complex that generates 800 lightning bolts is equivalent to TEN daily storms with 80 strikes. Then recall, the strikes you see at night don't count. You're counting thunder, so you can eliminate the bias of lightning being more visible at night.
In the end, the sunlight is clearly a dominant factor in timing, as confirmed by the data. Of course, the thunder is generally more frequent when the sun is providing the most energy for thundercloud development. Some days that energy is not utilized well (it is reflected by cloud cover, there is a massive inversion, the air is too dry, etc.). On average, though, that is when the greatest amount of lightning-generating cloud development will occur.