  The lattice model of the Weil representation over non-archimedean local field
$F$ of odd residual characteristic has been known for decades, and is used to
prove the Howe duality conjecture for unramified dual pairs when the residue
characteristic of $F$ is odd. In this paper, we will modify the lattice model
of the Weil representation so that it is defined independently of the residue
characteristic. Although to define the lattice model alone is not enough to
prove the Howe duality conjecture for even residual characteristic, we will
propose a couple of conjectural lemmas which imply the Howe duality conjecture
for unramified dual pairs for even residual characteristic. Also we will give a
proof of those lemmas for certain cases, which allow us to prove (a version of)
the Howe duality conjecture for even residual characteristic for a certain
class of representations for the dual pair $({\rm O}(2n), {\rm Sp}(2n))$, where
${\rm O}(2n)$ is unramified. We hope this paper serves as a first step toward a
proof of the Howe duality conjecture for even residual characteristic.
