  We propose a modification of the non-perturbative renormalization-group
(NPRG) which applies to lattice models. Contrary to the usual NPRG approach
where the initial condition of the RG flow is the mean-field solution, the
lattice NPRG uses the (local) limit of decoupled sites as the (initial)
reference system. In the long-distance limit, it is equivalent to the usual
NPRG formulation and therefore yields identical results for the critical
properties. We discuss both a lattice field theory defined on a $d$-dimensional
hypercubic lattice and classical spin systems. The simplest approximation, the
local potential approximation, is sufficient to obtain the critical temperature
and the magnetization of the 3D Ising, XY and Heisenberg models to an accuracy
of the order of one percent. We show how the local potential approximation can
be improved to include a non-zero anomalous dimension $\eta$ and discuss the
Berezinskii-Kosterlitz-Thouless transition of the 2D XY model on a square
lattice.
