Does an unlikely event make the existence of a god more likely? Maybe, but that might be the wrong way to think about it.
Let's approach this scientifically.
So we have an observation: a man asks God to strike him with lightning, and lightning strikes next to him.
One can't really conclude much from observation alone (rare events happen all the time), but we do have a hypothesis:
Hypothesis: asking God to strike you with lightning makes lightning strike next to you.
Supposing that asking God doesn't always work (because "you need enough faith", perhaps), we can modify this to: asking God to strike you with lightning makes it more likely that lightning will strike next to you.
In order to test this hypothesis, we can turn this into a scientific study, where you have one group of people who ask God, and one group who doesn't. Then you record lightning strikes and apply statistics to it to determine whether to accept the hypothesis with some probability.
Now lightning strikes are presumably too rare to get statistically significant results, but you could apply the same idea to more likely events, such as for healing, which people have done (and this "failed to produce significant findings").
Consider something else one might ask God for: asking God to help you find a job.
Let's say you're doing a cohort study instead of a controlled one (i.e. you just look at what happened instead of controlling anything). Now you very well may find a significant correlation between prayer and getting a job offer.
But one obvious confounding variable would be how much you want a job. If you really want a job, you may search harder and prepare better (so you're more likely to get a job offer), and you may also be more likely to pray. So any correlation you find between prayer and getting a job offer may simply be due to the fact that both are more likely when someone really wants a job.
If you consider believers who pray and non-believers, this would have the same problem. If you consider any believers and non-believers, there would still be confounding variables in terms of how employers view believers and non-believers, how wealthy the average believer or non-believer is, which resources or opportunities they might have access to (e.g. through their church), etc.
These things can be accounted for, but one should be aware of it before concluding anything.
What did we prove?
We could consider another case, which I've heard cited a few times by theists: asking God to help with addiction or depression.
In this case, one might even concede that prayer could work for this, but not because God exists. Instead, there may be some psychological benefits to putting some of one's burdens on someone else (even if they are merely imagined), from "knowing" there's someone looking out for you, from explicitly verbalising your desires, from taking some time to calm yourself, etc.
So if prayer has been proven to improve mental states, you still wouldn't be much closer to proving that God had anything to do with it.
If none of the above applies, then we might have some useful evidence.
You ask God for lightning, you get lightning (with statistical significance).
One could still say it's due to aliens with advanced technology, quantum stuff, any natural phenomenon that we're not familiar with yet, or psychic powers, and any given one of these explanations may be more or less likely, depending on the nature of the evidence. Different people would have different standards for when they'd accept it was a god instead of any of these things (or instead of simply sticking to "I don't know").
If one concludes that a god was responsible, the next obvious question would be: which god? There are multiple religions, and even within e.g. Christianity, there are vastly different beliefs of what God is like. So one would also need any evidence for a god to include details about that god. Otherwise you'd just be left with: some god exists, but I know nothing about them nor about what they want nor about what they offer, so their existence has no bearing on my life.
Theists can and do say God shall not be tested, but this would really be the only way to definitively reject the possibility of coincidence (even if it's much harder to definitively attribute things to God after rejecting coincidence).