  Let $\Omega$ be a pseudoconvex domain in $\mathbb C^n$ satisfying an
$f$-property for some function $f$. We show that the Bergman metric associated
to $\Omega$ has the lower bound $\tilde g(\delta_\Omega(z)^{-1})$ where
$\delta_\Omega(z)$ is the distance from $z$ to the boundary $\partial\Omega$
and $\tilde g$ is a specific function defined by $f$. This refines
Khanh-Zampieri's work in \cite{KZ12} with reducing the smoothness assumption of
the boundary.
