  We study the optimality of the remainder term in the two-term Weyl law for
the Dirichlet Laplacian within the class of Lipschitz regular subsets of
$\mathbb{R}^d$. In particular, for the short-time asymptotics of the trace of
the heat kernel we prove that the error term cannot be made quantitatively
better than little-$o$ of the second term.
