I've heard that lightning can strike miles from a storm, under blue skies. We've always taken that seriously and while we were hanging out at a friend's house this afternoon the second we heard thunder in the distance the kids were out of the pool. For hours storms passed miles away, and we finally thought it was about time to let the kids get back in.
I heard a loud crack behind me, and thought one of the neighbors had shot off a leftover firework from the 4th. Others that were sitting in front of me, facing out over the field behind me, had "that look" so I shot out of my chair and turned around. Above a row of trees about 200 yards away a black cloud of smoke was quickly blowing away. Lightning had struck one of those trees.
The nearest storm was many miles away. There were only high, thin clouds above us, no puffy cumulus clouds in sight. There was no rumble, just a single crack - like, I said, it sounded like someone set off a firework.
Moral of the story, yes, lightning can strike miles from a storm, under blue skies. Get out of the pool if you even think you hear thunder.