NP-hardness of computing lattice diameters of lattice polytopes

Let $d \geq 3$ and let $P$ be a lattice $d$-polytope. Lattice-polytope diameter conjecture. Computing a lattice diameter of $P$ is an $\operatorname{\mathsf{NP}}$-hard problem. This would extend the established NP-hardness result from bounded semi-algebraic sets, even when the diameter direction is fixed, to lattice polytopes.