  Hyperbolic vacuum black holes in Lovelock gravity theories of odd order $N$,
in which $N$ denotes the order of higher-curvature corrections, are known to
have the so-called isolated critical points with nonstandard critical exponents
(as $\alpha = 0$, $\beta = 1$, $\gamma = N-1$, and $\delta = N$), different
from those of mean-field critical exponents (with $\alpha = 0$, $\beta = 1/2$,
$\gamma = 1$, and $\delta = 3$). Motivated by this important observation, here,
we explore the consequences of taking the $D \to 4$ limit of Lovelock gravity
and the possibility of finding nonstandard critical exponents associated with
isolated critical points in four-dimensions by use of the four-dimensional
regularization technique, proposed recently by Glavan and Lin
\cite{Glavan2020}. To do so, we first present $\text{AdS}_4$ Einstein-Lovelock
black holes with fine-tuned Lovelock couplings in the regularized theory, which
is needed for our purpose. Next, it is shown that the regularized $4D$
Einstein-Lovelock gravity theories of odd order $N > 3$ do not possess any
physical isolated critical point, unlike the conventional Lovelock gravity. In
fact, the critical (inflection) points of the equation of state always occur
for the branch of black holes with negative entropy. The situation is quite
different for the case of the regularized $4D$ Einstein-Lovelock gravity with
cubic curvature corrections ($N=3$). In this case ($N=3$), although the entropy
is non-negative and the equation of state of hyperbolic vacuum black holes has
a nonstandard Taylor expansion about its inflection point, but there is no
criticality associated with this special point. At the inflection point, the
physical properties of the black hole system change drastically ...
