Why does power dip during a lightning storm?
Janka comes close, but there are are several more details.  (Note, recalling from EE classes about 45 years ago.)

On many high voltage lines there are arc electrodes at various points.  When lightning strikes the line, the increased voltage causes an arc to form across the electrodes.  This helps to dissipate the voltage of the lightning strike.

But the spacing of the electrodes is such that, once the arc has formed, the normal voltage on the line is sufficient to keep it going.  So the electrodes are formed in the classical V shape, close together at the bottom and wider at the top.

Heat causes the arc to rise (see "Jacob's ladder") and so it gets longer.  Eventually, when it gets to the top, the voltage will (hopefully) no longer sustain the arc.

If the arc does not extinguish itself, eventually a nearby over-current detector (fuse) will trip and cut off the power.

But to save the lineman a trip to reset it, the over-current detector is often designed with a timer so that it resets itself after a few seconds.  But usually there's a limit to how many times it will reset (in case the over-current condition is due to, eg, a downed power line).