If you drive to the store to buy a lottery ticket, you add a car to traffic. If you add a car to traffic, you adjust the timing of other people's traffic experiences. Someone hits one extra red light. They're now offset by 12 seconds from their baseline pattern. Things accumulate. It's hardly difficult to imagine how a tiny bit of noise results in a lot of differences. Again, I don't know the specifics of how lottery systems work, but if it's a pseudo random physical process with some degree of human input, I expect the butterfly effect would matter a lot. Dice are a good example. The amount of noise you need to add to make a parallel version of yourself roll differently on another timeline, even they both roll at exactly the same time, is probably trivial. Why? Because the human physical action is basically a random process in itself. Force, angle, hand position, landing angle, etc. People won't, and often can't, control these things with much precision and are largely driven by lots of tiny subconscious effects.

If an extra red light causes you to shake the dice or spin the balls an extra 0.1 seconds longer, it seems likely that the outcome will be different.