  LaCrGe$_3$ has attracted attention as a potential candidate for studies of
quantum phase transitions in a ferromagnetic material. The application of
pressure avoids a quantum critical point by developing a new magnetic phase. It
was suggested that the disorder may provide an alternative route to a quantum
critical point. We used low-temperature 2.5 MeV electron irradiation to induce
relatively small amounts of point-like disorder in single crystals of
LaCrGe$_3$. Irradiation leads to an increase of the resistivity at all
temperatures with some deviation from the Matthiessen rule. Hall effect
measurements show that electron irradiation does not cause any detectable
change in the carrier density. Unexpectedly, the Curie temperature,
$T_{\text{FM}}$, \emph{increases} with the increase of disorder from
approximately 90 K in pristine samples up to nearly 100 K in the heavily
irradiated sample, with a tendency towards saturation at higher doses. Although
the mechanism of this effect is not entirely clear, we conclude that it cannot
be caused by effective ``doping" or ``pressure" due to electron irradiation. We
suggest that disorder-induced broadening of a sharp peak in the density of
states, $D(E)$, situated at $E_p=E_F-0.25$ eV below the Fermi energy, $E_F$,
causes an increase in $D(E_F)$, leading to an enhancement of $T_\text{FM}$ in
this itinerant ferromagnet.
