Simple B-free lattice systems are a multi-dimensional generalisation of Erdoes B-free numbers. They have interesting symmetries, and one can compute their spectra with respect to the Mirsky measure explicitly, including a closed formula for the corresponding eigenfunctions. The latter rests upon a uniform distribution result in the context of their description as weak model sets. This approach can be extended to also cover the point part of the spectrum with respect to the measure of maximal entropy, via Kolmogorov's strong law of large numbers. Most of these features can be explained via an example based on the visible points of a lattice.