Beane's experiment centers around observing high energy processes, such as those involving cosmic rays. These processes become smaller the more energetic they are. In a simulation, once the processes shrink to the size of the lattice, they cannot shrink further, and thus there should be a cutoff for how much energy can be applied to the system.
As it happens, there is indeed an upper limit to how much energy can be applied; this is what GZK is. It's a well studied phenomenon – when enough energy is applied to cosmic rays, background microwave radiation begins interacting with them, preventing them from attaining more energy. However, this doesn't necessarily mean we live in a simulation; it all has to do with how the physics surrounding the GZK behave. If they behave as they should, Beane believes his team will be able to see this; but he also believes that if we are simulated, that he should be able to see the lattice.
This is what GZK looks like
Of course, whether we find a lattice or not won't necessarily determine if we're simulated. There's no guarantee an advanced civilization would use technology even remotely similar to ours for their science projects.