Fire created by lightning will stay on forever even if rain is pouring down over it. It can only be extinguished manually, but doesn't affect players.
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Thanks Caleb I've never noticed it couldn't hurt the players I've updated the description an title.
I can confirm this, It happens to me all the time.
The only way to get rid of the flame is by placing a block on top of it.
Its basically a ghost flame (you can't get injured from it)