When I hit mobs and players in the rain with fire aspect they would still continue taking fire damage after and may or may not show that they are on fire. This can also happen when something walks onto a campfire. I do not know if this could happen with lava, fire, or with a flame bow. Also a drowned also walked out of the water in the rain and was taking fire damage. I don’t have a video where the mobs take fire damage when hit with a fire aspect sword but I do have a video of mobs taking fire damage in the rain.