  We consider the dynamics of lattice random walks with resetting. The walker
moving randomly on a lattice of arbitrary dimensions resets at every time step
to a given site with a constant probability $r$. We construct a discrete
renewal equation and present closed-form expressions for different quantities
of the resetting dynamics in terms of the underlying reset-free propagator or
Green's function. We apply our formalism to the biased random walk dynamics in
one-dimensional unbounded space and show how one recovers in the continuous
limits results for diffusion with resetting. The resetting dynamics of biased
random walker in one-dimensional domain bounded with periodic and reflecting
boundaries is also analyzed. Depending on the bias the first-passage
probability in periodic domain shows multi-fold non-monotonicity as $r$ is
varied. Finally, we apply our formalism to study the transmission dynamics of
two lattice walkers with resetting in one-dimensional domain bounded by
periodic and reflecting boundaries. The probability of a definite transmission
between the walkers shows non-monotonic behavior as the resetting probabilities
are varied.
