  We analytically study stability of sliding lattice of Josephson vortices
driven by a transport current in the stack direction in strong in-plane
magnetic field. In contrast to recent findings we obtain that there are no
diverse configurations of stable vortex lattices, and, hence, the stable
sliding vortex lattice can not be selected by boundary conditions. We find that
only the triangular (rhombic) lattice can be stable, its stability being
limited by a critical velocity value. At higher velocities there are no simple
stable lattices with single flux line per unit cell. Oblique sliding lattices
are found to be never stable. Instability of such lattices is revealed beyond
the linear approximation in perturbations of the lattice.
