  We combine classical Vinberg's algorithms with the
lattice-theoretic/arithmetic approach from arXiv:1706.05734 [math.AG] to give a
method of classifying large line configurations on complex quasi-polarized
K3-surfaces. We apply our method to classify all complex K3-octic surfaces with
at worst Du Val singularities and at least 32 lines. The upper bound on the
number of lines is 36, as in the smooth case, with at most 32 lines if the
singular locus is non-empty.
