  Suppose $X$ is a locally compact Polish space, and $G$ is a group of lattice
isometries of $C_0(X)$ which satisfies certain conditions. Then we can equip
$C_0(X)$ with an equivalent lattice norm $| \! | \! | \cdot | \! | \! |$ so
that $G$ is the group of lattice isometries of $(C_0(X), | \! | \! | \cdot | \!
| \! |)$. As an application, we show that for any locally compact Polish group
$G$ there exists a locally compact Polish space $X$, and an lattice norm $| \!
| \! | \cdot | \! | \! |$ on $C_0(X)$, so that $G$ is the group of lattice
isometries of $(C_0(X), | \! | \! | \cdot | \! | \! |)$.
