  We establish in this paper the logarithmic Bramson correction for Fisher-KPP
equations on the lattice $\mathbb{Z}$. The level sets of solutions with
step-like initial conditions are located at position
$c_*t-\frac{3}{2\lambda_*}\ln t+\mathcal{O}(1)$ as $t\rightarrow+\infty$ for
some explicit positive constants $c_*$ and $\lambda_*$. This extends a
well-known result of Bramson in the continuous setting to the discrete case
using only PDE arguments. A by-product of our analysis also gives that the
solutions approach the family of logarithmically shifted traveling front
solutions with minimal wave speed $c_*$ uniformly on the positive integers, and
that the solutions converge along their level sets to the minimal traveling
front for large times.
