We don't know how it actually happens. The mechanisms we know for building up charge separation in clouds should not produce fields strong enough to initiate lighting, and measurements back that up. The fields are too weak by an order of magnitude.

We don't know if there is some other mechanism that produces stronger fields locally that gets lightning started, or if something lowers the required field strength, or maybe something else.

Here is a recent article on a new mechanism that may have something to do with it, and that casts doubt on a theory that has been popular for a couple decades [1].

Here's another article that mentions that, and mentions some of the other lightning mysteries [2].

[1] https://phys.org/news/2016-02-scientists-clues-mystery-light...

[2] http://voices.nationalgeographic.org/2017/05/02/unraveling-t...

There are also some signs of radiation and neutron emission around thunderstorms.

Nature is cool.