That’s because hurricanes don’t really have a lot of lightning. But why?

The reason is that thunderstorms are up-down things, and hurricanes are round-and-round things. The updownness of winds in thunderstorms causes ice and water droplets to interact in a way not totally different from a balloon rubbing against a wool sweater, causing a charge differential to build up, with the upper parts of the forming thunderclouds being more positive than the lower parts (and the ground). Lightning is the discharge across that differential.

That up-down dynamic does exist in hurricanes, and there is some lightning and thunder, just not much. Most of the energy dynamic in a thunderstorm is rapid uplift of air into the thunderhead, so the thunderstorm is all about forming a charge differential. Most of the energy dynamic in a hurricane is much larger scale, much more horizontal.

It may be the case that lightning is most likely to develop along the eye wall of the strongest hurricanes. Emily, a 2005 Category 5 hurricane, was seen to have an unusual amount of lightning in the eye wall, and that prompted further research into the phenomenon. Katrina, Andrew and Rita had a lot of lighting around the eye. It has been suggested that lightning activity along the eye wall picks up when a strong hurricane is increasing in strength. So there is a hurricane-lightning link, but thunderstorms are major lightning machines.

NASA Finds Intense Lightning Activity Around a Hurricane’s Eye

Maximum hurricane intensity preceded by increase in lightning frequency

Polarity and energetics of inner core lightning in three intense North Atlantic hurricanes

The Morphology of Eyewall Lightning Outbreaks in Two Category 5 Hurricanes