Hey there. The explosive runes card reads "Play this card after a hero opens a door or searches." So the triggering condition to this card is the "Open door" action and the "Search" action that heroes can perform.
In the Siege of Skytower, pulling a lever is a "Special" action. The effect of this action is that one door will close, and another will open if it was previously closed. This is a quest specific mechanic that causes doors to open/close, but it is only an effect caused by pulling levers.
In this case, I would rule that the triggering condition is not met and therefore the Overlord can't use the card.