So, a few things. Bearing in mind that I am not by any means an expert in lightning formation or the power grid.
First, what is lightning? Lightning is an electrical discharge; it's a type of dielectric breakdown that occurs when the potential difference (e.g. voltage) between clouds and the ground or between two clouds is high enough to overcome the dielectric effects of air. Clouds tend to
accumulate electrostatic charges (positive at the top and negative at the bottom) for reasons I am not qualified to explain. The air becomes ionized and forms a plasma, which is electrically conductive - lightning. In the process, the electrical charge at the two ends of the lightning strike will become (more or less) equal. For our purposes we will ignore cloud-to-cloud strikes, even though I believe they outnumber cloud-to-ground strikes.
Note that cloud-to-ground strikes may involve either the negatively-charged lower region of the cloud or the positively-charged upper region; for simplicity, and because they make up the large majority of such strikes, we are only going to worry about strikes involving the negatively-charged part of the cloud.
Second, where does lightning strike? If the Earth were a perfect sphere, with a perfectly uniform shell of clouds above it, with perfectly evenly distributed charge on each, and if the air were a perfectly uniform dielectric between them... then the probability of a lightning strike would be equal in all places. But those assumptions are not true. The Earth's surface is uneven, in part due to man-made artifacts like buildings. The distribution of clouds is uneven. The distribution of charge on each is uneven. And the dielectric properties of air vary considerably with factors like humidity. So this creates a non-uniform probability distribution for lightning strikes. A very tall building will be struck more often than the ground around it. This is why, after all, you should not stand in an empty field during a thunderstorm.
But recall that, at the moment of the strike, the charge between the object on the ground and the (region of the) cloud is equalized. This means that another strike from the same cloud to the same area on the ground is unlikely until charge can re-accumulate. And as clouds have vaguely similar charge distributions, the charge on the ground should now be closer to that of the other clouds, so a strike from the other clouds to the same point on the ground is also less likely.
So, for a period of time, lightning is in fact
less likely to strike the same place twice. But that effect is pretty localized, and only lasts for a limited time (my guess would be minutes, maybe hours). Certainly not years.
Third, and this is important to your particular line of questioning, how does lightning disrupt the power grid? The popular notion is that when lightning strikes part of the electrical grid this electrical transient is conducted directly to home devices attached to the grid. And this can happen. But to my understanding the more common cause is that the strike causes a component of the grid to fail or shutdown, which still results in ugly transients but is less extreme. Or the lightning may cause a secondary effect that impacts the grid; for example, a strike may hit and knock down a tree, which damages equipment (often cables) as it falls.
To the best of my understanding, failures due to downed trees are actually the primary cause of outages. And I believe strikes on power lines (of which there are a lot, usually suspended up in the air) are more common than strikes on ground equipment like substations, although both power lines and ground equipment have a variety of protections intended to prevent outages or damage.
TL;DR: Does lightning really not strike twice?
Lightning does strike twice, but usually not immediately.