A Lattice-Boltzmann approach is used to simulate the aerodynamics of complex three-dimensional ice shapes on a NACA 23012 airfoil. The digitally produced high fidelity geometrical ice shapes were created using a novel laser scanning technique in the NASA Icing Research Tunnel. The geometrically fully resolved unsteady simulations are conducted on two ice shapes representing a roughness type and a horn type icing on the leading edge of the airfoil. Comparisons between simulation and experiment of lift, drag, and pitching moment as well as pressure distributions indicate overall a good qualitative agreement in capturing the aerodynamic degradation. Especially for the horn-type ice shape, the quantitative agreement is also mostly very good. Analysis of the flow structures indicates furthermore a good capturing of the three-dimensional separation behavior of the flow.