This is similar to the problem of the best way to shuffle a deck of cards. I think that, generally speaking, these types of mixing techniques (similar to just spreading out a deck of cards and making a mess pushing them around) are actually quite good at eliminating correlations if they are done for enough time. You are right in that this system is primarily governed by Newtonian mechanics, such that if you knew the initial conditions of the system well enough and had a powerful enough computer, you could probably predict the result, but for practical purposes this isn't so important. There are probably numerous ways of rigging a machine like this as well.
Some things that would make it less random include using fewer balls, having a smaller disk for them to move around in, and swirling the disk for a shorter period of time. Doing the experiment in vacuum would probably make the system a little easier to calculate, but again something like this would still be so difficult to calculate (you'd also have to very precisely know e.g. the location and structure of rough spots on the disk and the balls) that it isn't very important for anyone who actually cares about winning the lottery.