BABIP reflects a certain combination of batting skills. Some players maintain a high one (Joe Mauer), some maintain a low one (Max Kepler) - just as some players hit homers and others don't.
Coming into this season, among players with at least 2000 PA (to try to rule out small samples, which obviously biases toward good players) across the past ten seasons, Brandon Marsh maintained a .371 BABIP. (He's "down" to .339 this season.) Austin Hedges, in case anyone's curious, is low man among these 296 players, with .238.
When someone's on a hot streak, almost certainly some components of his game will be outside his usual norms. If for instance the strikeouts are suddenly low, you could expect regression to his prior mean - but there do exist players who don't strike out very much, and fans of the player could hope that he's found some new tactic that cuts down the Ks permanently. Similarly if the HRs are suddenly up at some kind of Kyle Schwarber rate, probably it's just a fluke, but maybe our hero has unlocked something that will continue, because there do exist players who have that kind of production. Walks, ditto - batters with great eyes exist, and maybe the guy on a good run has joined their ranks.
So, my point really is just that the tear Lewis has been on is supported by something, a .484 BABIP, that is literally .100 higher than any major leaguer has been able to maintain on a long term basis the past ten years. It would be one thing if we thought Lewis had suddenly become Brandon Marsh. It's another, if we thought he became Kal-El of Krypton come to Earth
Players tinker with their plate approach all the time. They're trying to get better, they're trying to confound the "book" that opposing teams have on him. The opposing teams tinker with the "book" on him, in response. Health and any number of factors play in as well.
Thus I don't call it luck. Lewis is trying his best on every at bat, and the opposing pitcher is trying his best on every throw he makes. Let the best man win.
But the rate of success Lewis is enjoying isn't based on the kind of thing that continues indefinitely.