The electric fields in thunderstorms can exceed the breakdown value locally near ice particles present in thunderclouds. But are fields high enough and the regions large enough to initiate a streamer discharge? And where would a sufficient density of free electrons come from to start the discharge in the humid air that rapidly binds electrons in water-clusters?
Cosmic Lightning
International Conference on Phenomena in Ionized Gases
Multiscale Dynamics

A. Dubinova, A., Rutjes, C., Ebert, U., Buitink, S., Scholten, O., & Trinh, G. (2015). Lightning inception from ice particles and extensive air showers. In Proceedings of International Conference on Phenomena in Ionized Gases 2015 (ICPIG 32) (pp. 1–4).