I watched the anime at least twice but I don't understand. I know Dragon saved Luffy from Smoker but did he save Luffy at the execution stand? Bartholomew said he was stunned when he saw the lightning save Luffy. That makes me think it was Luffy's unexplainable luck, like when Fujitora rolled the dice to pursue Luffy
To answer cannonically, no he did not. As far as we know Dragon was not involved in that scenario and the reason why he survived is because of his incredibly high luck.
To answer speculatingly, There is some suspicion that this luck stems from the fact that he carries the "Will of D" whereas he must be an integral person to change the world.
The truth is however, given that he series is still in production (and probably will be for some time). We do not have enough data to say true or false. We can only form opinions off of what we do know.
I do not know if this is accurate, of course as Kaz suggested only time can tell for sure. I compared the anime and manga and realized a few differences;
Anime messed the timing, they probably were not expecting the "Will of D" at this time. Nami noticed the storm before Luffy was pinned at the execution stand (Chapter 98). In the Anime, Nami noticed the storm after Luffy was pinned (Episode 52). Leading me to consider the storm was either natural or if Dragon was a fruit-eater (only an one-piece fan would understand "fruit-eater") it was unintentional.
It is obvious Dragon saved Luffy from Smoker. Anime makes it look like Dragon caused the Gust which freed Buggy, Alvida and the Mugi-wara (Straw hat) crew (Episode 53). However in the Manga (Chapter 100), the gust seems to have caught even Dragon by surprise.
When Smoker pins Luffy, he tells Luffy that "Luffy's luck has run out" in the Manga (Chapter 100), but Smoker says his own bad luck has ended in the Anime (Episode 53)
Therefore I think the lightning which saved Luffy was Coincidental, "Will of D" or "Luck"