Vertex distortion of lattice knots

The vertex distortion of a conformation of a lattice knot is the supremum of the ratio of the distance between a pair of vertices along the knot and the distance in the L1 norm. We generalize results of Gromov and Pardon about the distortion of smooth knots and show that the distortion of a lattice knot is 1 if and only if it is the unknot and that there are minimal stick number knot conformations with arbitrarily high distance.