Here we show that spin-lattices can serve as a test object for quantum foundations and quantum information theory, revealing unsuspected properties. We propose a (thought) experiment on such lattices that mimics the Bell-experiment and calculate the outcomes and the Bell inequality. It appears that for a wide range of geometries the Bell-inequality is violated, even if these lattices are local according to the usual definitions. Some spin-1/2 lattices can even violate the Bell inequality more than the Tsirelson bound. We argue that there is no consensual explanation for this result. We make the link with problems in quantum foundations and quantum information theory.