Bremsstrahlung refers to the energy radiated away, in this case by gamma rays, when a charged particle undergoes some acceleration--or sudden deceleration. If you accelerate a bunch of electrons to high energy and then stop them suddenly you'll get a lot of radiation. If the photons that result are high enough energy (a bit more than 1MeV) and one comes close enough to a nucleus it can "pair-produce": create an electron and positron. That positron may escape, if the air density is low enough, but most will slow down and annihilate with an electron to produce two photons with energy 511KeV each. When you see a lot of those photons, you know something is producing antimatter. And you know there was a lot more energy that you didn't see.
We see these positrons--sometimes. One especially bright burst was estimated to have produced 10^14 positrons--and those are orders of magnitude fewer than the fast electrons that started the show.
Lightning doesn't always produce gamma rays O(.002)% Sometimes the gamma ray bursts are milliseconds long, and sometimes they can glow for several minutes. "During a winter thunderstorm in Japan on 9 January 2018, our detectors caught a gamma-ray glow, which moved for ~100 s with ambient wind, and then abruptly ceased with a lightning discharge." That sounds as though the process that creates these also sparks lightning, not lightning producing the acceleration. At least for the slow process. I have no idea what might be causing that.
Maybe the 1ms bursts do come with or after lightning--the time scale seems to match better. If the superheated plasma's density dropped enough, maybe there would be enough residual field to accelerate electrons through the channel, and the density be low enough to keep them from scattering and losing energy too quickly? Near the lightning channel fields can reach about 1MV/meter. Of course, the inch-wide lightning channel isn't very straight, even on the scale of meters. Figure 10.3 in that link shows jags on the scale of a couple of inches! I'm not sure of the structure of the lightning channel, but I'd think electrons of the energy we want here would be apt to go straight and not follow the bends in the channel--and thus not get accelerated for long before hitting relatively dense air.
This would be a fun subject to study. Maybe the Japanese approach will be cheap enough that they can get triangulation and start to see what part of the cloud the glows come from.
FWIW, the interactions of high enough energy gamma rays (and presumably electrons also) can force nuclear reactions in atmospheric nuclei--possibly comprising one source of C14.