Both your sentences are problematic.
"In" indicates presence. Like, "The dog is IN the house." "Into" indicates direction. Like, "The dog ran INTO the house."
And as I write that second example I realize there's an ambiguity. You could say, "The dog ran in the house." But it wouldn't mean the same thing. "The dog ran into the house" means he was someplace else, someplace outside the house, and then he entered the house. "The dog ran in the house" means he was in the house the entire time, running around.
So "... gulping ... air in his lungs" doesn't really make sense. The air came from outside and was brought inside. You need to indicate direction. "Into" is a valid preposition. "... gulping ... air in his lungs" would mean that the air was already in his lungs, which probably isn't what you want to say.
"... gulping in ... air into his lungs" The "in" is unnecessary. A fluent speaker MIGHT say this because we sometimes say "gulping in" as a sort of idiom. But it's just a wasted extra word that doesn't really add any meaning to the sentence.