  In this paper, we show that for sufficiently strong atomic interactions,
there exist analytical solutions of current-carrying nonlinear Bloch states at
the Brillouin zone edge to the model of spin-orbit-coupled Bose-Einstein
condensates (BECs) with symmetric spin interaction loaded into optical
lattices. These simple but generic exact solutions provide an analytical
demonstration of some intriguing properties which have neither an analog in the
regular BEC lattice systems nor in the uniform spin-orbit-coupled BEC systems.
It is an analytical example for understanding the superfluid and other related
properties of the spin-orbit-coupled BEC lattice systems.
