We all know Þórr means thunder and that Mjǫllnir may possibly mean lightning, however, in all the texts I've read, there isn't a single mention (or at least not a relevant one) of a connection between the mighty God and lightning bolts. I know that there was an association between him (actually *Þunraz, I think) and Jupiter, which is shown in the week days in most romance languages (such as in italian "giovedì "[Jupiter's day]) and most Germanic languages (such as english "Thursday") -- the famous interpretātiō germānica. Did the norseman believed that Thor, during the Viking Age, was really a storm-related God or was it a belief that vinished through time and is reserved to *Þunraz?
The 11th century Christian missionary Adam of Bremen wrote,
"Thor, they say, presides over the air, he governs the thunder and lightning. the winds and rains."
The Norse believed that during a thunderstorm, Thor rode through the heavens on his chariot pulled forward by the goats Tanngrisnir ("gap-tooth") and Tanngnjóstr ("tooth grinder"). Lightning dashed whenever he threw his hammer Mjölnir.
Some good information about the viking age can be gotten from this treatise. wikipedia to Gesta Hammaburgensis ecclesiae pontificum
In the Netherlands we have Donar (West German Thor), and here the story always went that when there was a thunderstorm Donar rode his chariot across the sky while slamming his hammer around making lightning.