There are many modelling studies I can find at first glance, eg this one (including references to older studies): https://www.nature.com/articles/s41558-018-00

There are many modelling studies I can find at first glance, eg this one (including references to older studies): https://www.nature.com/articles/s41558-018-0072-6 https://www.nature.com/articles/s41558-018-0072-6 > 'Most previous studies project an increase in global lightning with climate change over the coming century, but these typically use parameterizations of lightning that neglect cloud ice fluxes, a component generally considered to be fundamental to thunderstorm charging. As such, the response of lightning to climate change is uncertain. [...] In contrast to the previously reported global increase in lightning based on CTH, we find a 15% decrease in total lightning flash rate with IFLUX in 2100 under a strong global warming scenario.' or eg this one using data: https://www.sciencedirect.com/science/article/abs/pii/S1364682618306229?via%3Dihub https://www.sciencedirect.com/science/article/abs/pii/S13646... > 'Many published analyses show that lightning activity is responsive to temperature on time scales ranging from the diurnal to the decadal. The hiatus in global warming is manifest in several global datasets in the decadal period 2002–2013. The statistically flat behavior of the global lightning record from the NASA Lightning Imaging Sensor over the same period is consistent with this hiatus in global warming.'