  We prove a lower bound on the eigenvalues $\lambda_k$, $k\in\mathbb{N}$, of
the Dirichlet Laplacian of a bounded domain $\Omega\subset\mathbb{R}^n$ of
volume $V$: $$ \lambda_k \geq C_n\bigg( \delta\frac{k}{V}\bigg)^{2/n} $$ where
$\delta$ is a constant that measures how efficiently $\Omega$ can be packed
into $\mathbb{R}^n$ and $C_n$ is the constant found in Weyl's law. This
generalizes a result of Urakawa in 1984. If $\delta^{2/n} > n/(n+2)$, this
bound is stronger than the eigenvalue bound proven by Li and Yau in 1983. For
example, in the case of convex planar domains, we have for all
$k\in\mathbb{N}$, $$ \lambda_k \geq \frac{2\sqrt{3}\pi k}{V}. $$
