In Back to the Future, how did Marty get the timing right with the lightning strike?

What makes you think the lightning could strike before the clock tower was grounded (by Doc plugging the cables back together, the metal poles beside the road providing a path to ground). Things to note:

• When the plug near the ground pops loose, the free end is stuck in a tree, not too close to the ground, so not a great path to ground.
• Lightning is striking all around and near the lightning arrestor above the clock. Any of those could have done the job, but they require a path to ground.
• The lightning completely stops after the useful bolt. Who's to say there isn't a flying train in the clouds firing a lightning gun at the tower until success is achieved? (That's far more likely to work than waiting for nature to do it.)

There's no logic explanation for this, it's just a plot hole created by the need of giving more tension on the end of the movie. Maybe if the horizontal wire could stretch a lot while the car runs after the connection with the hook, but i doubt it.

We know that the timer went off several seconds before Marty floored the accelerator. We know that Marty quite literally hooked the line at precisely the correct time. Therefore the only valid conclusion is that Marty accelerated faster than Doc calculated/anticipated/intended.

Thus there are only two valid explanations:

(1) Doc planned for Marty to accelerate at a rate less than the car's maximum acceleration. This leads to the obvious question: How would Marty know how fast to accelerate? We can suppose that he did some test runs off screen, or we can attribute it to movie magic ("he eyeballed it!").

(2) Doc miscalculated the maximum acceleration of the car. Although a genius, perhaps there were aspects of the car that he had no way of determining in advance. Or maybe there was less fuel in the tank (less mass to push) or better road traction than he anticipated (although the roads seemed pretty slick, IMO). Either way, if he did make a mistake and the timer was set to assume maximum acceleration, then Marty was very lucky.

There is a third option (Marty was always supposed to wait X number of seconds after the timer went off), but that isn't directly supported by anything canonical in the movie.

Other thoughts:

The flexibility of the hooking mechanism or any other such variance in exactly when Marty hit the cable is negligible. He clearly left the starting line many seconds late. Any question about whether the flexibility of the hooking mechanism impacted his arrival time would only have an impact on the order of milliseconds and may thus be discounted for the purpose of this question.

The speed of the lightning through the cable is obviously shown to be quite slow for visual impact in the movie. Obviously in real life it would have traveled faster than that. In any event, Doc would have been able to calculate the speed of the lightning through the conductor, so let's assume he was accurate there.

Unfortunately any discussion surround whether the lighting struck at "precisely" 10:04:00 or sometime between 10:04:01 and 10:04:59 is a red herring. The fact is that the movie depicts the lightning as striking immediately after the minute hand moves to 10:04. It's not made clear in the movie how 1955 Doc knows that it will be "precisely" 10:04:00. (My guess: clock engineers in the intervening years investigated the clock, observed that it was "precisely" 10:04:00, and then documented that fact in the flyer that Marty received. But exactly how that information came to Doc is beyond the scope of the question the OP asked.) Regardless, 1955 Doc is correct -- lightning did strike at precisely that time.

It's a paradox. Predestination Paradox to be precise. The Lightning only strikes the Clock Tower because of the changes Doc and Marty make in order to harness the power of the Lightning Strike. The exact time of the Strike didn't matter, because while Doc and Marty are aiming for that exact minute based on the paper/their "history", whatever they actually do becomes the time that the Clock Tower is struck.

See: Twin Pines Mall become Lone Pine Mall,

For an in-universe explanation: There may be sufficient capacitance in the system to allow the lightning charge to be stored for one minute.

Doc Brown only knew the the lightning strike to +/- one minute, so it is logical that he would calculate the capacitance of the clock tower, and add additional capacitance to into the circuit to cover one minute of time.

But would that even be possible? To determine this we need to know how much power could be stored in the capacitor, and how much power the time machine needed.

The DeLorean's flux capacitor needs 1.21 gigawatts. But gigawatts is power over time, and we don't know how long the time machine needed that supply. Watching the video of the first time travel back to 1955, there is some bright light then Marty appeared back in time instantly. The video is 24fps, so "instantly" is less than 1/24th. 1/24th of a second times 1.21 gigawatts is 50.4 megajoules.

Oh this is gonna work out great...

The worlds largest capacitor is currently 50 megajoules! That is much less than a bolt of lightning. Now, I dunno how Doc Brown could make a 50 megajoule capacitor on his own. But the guy built a time machine so let's give him this one.

One more point: The "antennae hook" mechanism that attached to the car had some bend in it, so if Marty arrived a few seconds too soon the hook would remain connected to the wire long enough to catch the lightning.

The short answer is that (at least according to the film's official novelisation, based on the original screenplay) Marty has been practicing his run and has worked out a slightly faster route than the one planned by the Doc. This allows him to hit the wire at exactly the right moment, despite having lost time trying to get the DeLorean restarted.

“Damn!” he repeated, this time in a loud and clear voice. Moving away from the curb into the center of the street, he grunted as he saw a car moving toward him with precipitous speed.
“Good,” he grunted finally, satisfied that the vehicle was his Packard. “But why drive like that, dummy? Why crack up in the wrong car?”
A moment later, Marty was available for the answer. Dressed in his 1985 clothes, he pulled Doc’s car to the curb, leaped out, took a deep breath and smiled a bit sheepishly. “You’re late!” Doc Brown scolded. “Do you have no concept of time?”
“Sorry, Doc.”
“And why were you driving my car like a maniac?”
“It was a test. I wanted to see how fast I could go on that stretch. And I’m glad I did. There’s a rise in the road down near Cherry Street that’s almost like a speed bump. If I’d hit that at a higher speed, it could have sent me into a store window. But if I use the left side of the road it’ll be O.K.”

Futurepedia tells us that:

the flyer [Marty] was given by the Hill Valley Preservation Society, announc[ed] that the Courthouse would be struck by lightning at 10:04 pm that next Saturday night.

Now, the assumption made throughout the movie is that the lightning would strike at exactly 10:04 PM, but what's the chance that it would be precisely that moment? Note that the flyer says '10:04 pm', not '10:04:00'pm, simply because they wouldn't have known the precise second it struck. My thinking has always been that the lightning struck sometime slightly after 10:04 pm, so although Marty didn't leave at precisely the right time that Doc had calculated (under the assumption that the lightning would strike at precisely 10:04 pm), the time that Marty left (through movie magic no doubt) was just right for the DeLorean to make contact for the lightning to feed into the flux capacitor.

There are many possible explanations, but now that I think of it, the most probable is that Doc calculated the start time based not on the maximum acceleration of the car, but on some lower one. It doesn't make sense to hit the gas at the latest moment possible, because a slightest mishap will be fatal. So Doc allowed some leeway in his design.

Marty obviously had to hit the gas harder than they agreed before to make up for the lost time. Of course, there still is an element of luck (what if he hits it harder than necessary?), but it would be there anyway.

Who is the single witness to the lightning striking the clock tower and the person able to write down the exact time of the the strike? Doc himself. And Doc in 1955 (before the lightning happens) has the brochure from the 1985 where the time of lightning is stated. This makes the whole event of getting the timing right possible. If Doc in 1955 can figure out that the info in the brochure from 1985 will have originated from his statements as the single witness, than he will know by the wording in the brochure exactly what time the lightning will happen, that's why he will confidently utter the sentence "the lightning will strike at precicely 10:04 pm" (he is a scientist, right, he knows that if it was 10:04:31 it happened, the brochure would state it like that, because the time of the event has been written down from his mouth, and he would state the precise, scientifical time as he is a scientist). But I guess he also needs to take some more precautions for the plan to work, I guess that he will put in some slack as already mentioned with the stretching of the wire etc like some people already mentioned to deal with timing problems like delayed start of the car etc. Now after he has sent Marty back to 1985, he has to write down the exact time of the lightning and make sure his witness-story with the time is the one being collected so that the brochure will contain the correct, precise time for the lightning-plan to work when Marty travels to 1955 :-P

This might have another explanation, involving the "sentient flux capacitor" theory. This theory is not canon but provides an interesting development about the whole series of movies.

As a time regulation mechanism, the flux capacitor must prevents paradoxes and thus, in order to get marty back to his own time, it prevents the car from starting just long enough so it touches the cable at the exact right time compensating marty's driving or Doc's calculations errors.

You can see here more examples supporting this theory Thinking of the flux capacitor as a sentient entity really makes you see the ending of the third film in a different and kind of sad way.