  A long-standing conjecture of Lapidus claims that under certain conditions,
self-similar fractal sets fail to be Minkowski measurable if and only if they
are of lattice type. The theorem was established for fractal subsets of
$\mathbb{R}$ by Falconer, Lapidus and v.~Frankenhuijsen, and the forward
direction was shown for fractal subsets of $\mathbb{R}^d$, $d \geq 2$, by
Gatzouras. Since then, much effort has been made to prove the converse. In this
paper, we prove a partial converse by means of renewal theory. Our proof allows
us to recover several previous results in this regard, but is much shorter and
extends to a more general setting; several technical conditions appearing in
previous versions of this result have now been removed.
