  We prove that for $n\geq 2$, a non-uniform lattice in $\text{PU}(n,1)$ does
not admit a relatively geometric action on a $\mathrm{CAT}(0)$ cube complex, in
the sense of Einstein and Groves. As a consequence, if $\Gamma$ is a
non-uniform lattice in a non-compact semisimple Lie group $G$ without compact
factors that admits a relatively geometric action on a $\mathrm{CAT}(0)$ cube
complex, then $G$ is commensurable with $\text{SO}(n,1)$. We also prove that if
a K\"ahler group is hyperbolic relative to residually finite parabolic
subgroups, and acts relatively geometrically on a $\mathrm{CAT}(0)$ cube
complex, then it is virtually a surface group.
