It is just a sequence of when to increase the bet size. It has nothing to do with luck. If you lose a bet and double your betting amount does it influence the next bet? It does not because the house edge remains same and it just a new bet every time, the seeds remain same.
It has everything to do with luck. Bets are all independent of each other, but that doesn't mean that they aren't influenced by luck. If you encounter a long losing streak, you get screwed royally.
However, if you encounter a long winning streak, you could get rich overnight by doubling down on every bet and stopping at the right moment. Streaks <-> Luck!