If lightning strikes a Pig or Villager, you stop possessing the creature as it transforms, but unlike other transformations, you do not automatically start possessing the transformed creature. You also do not get the Attrition effect.

Other transformation:

1. Be in the Overworld.
2. /summon piglin
3. Possess the piglin.
4. Wait until the piglin converts.
5. (✔️) Notice that you are now possessing the resultant Zombified Piglin.

Lightning bolt transformation case 1:

1. /summon pig or /summon villager
2. Possess the pig or villager
3. /summon minecraft:lightning_bolt ~3 ~ ~
4. (❌) Notice that you stop possessing the resultant Zombified Piglin or Witch.

Lightning bolt transformation case 2:

1. /summon mooshroom
2. Possess the mooshroom.
3. /execute as @e[limit=2] run summon minecraft:lightning_bolt ~3 ~ ~
4. (✔️) Notice that the mooshroom transforms a lot, but you still retain possession throughout these transformations.

Modlist (MC 1.16.5):

Mods:
  [✔️] fabric-api-0.29.3+1.16
  [✔️] modmenu-1.14.13+build.19
  [❌] requiem-1.4.4.jar (disabled)
  [❌] requiem-1.5.0.jar (disabled)
  [❌] requiem-1.6.2.jar (disabled)
  [❌] requiem-1.7.0.jar (disabled)
  [✔️] requiem-1.7.6
  [❌] requiem-pandemonium-1.4.4.jar (disabled)
  [❌] requiem-pandemonium-1.5.0.jar (disabled)
  [❌] requiem-pandemonium-1.6.2.jar (disabled)
  [❌] requiem-pandemonium-1.7.0.jar (disabled)
  [✔️] requiem-pandemonium-1.7.6