  We show that the scalar-tensor theory that arises in a rigorous $D \to 3$
limit of Lovelock gravity up to cubic order admits a holographic c-theorem and
verify that the value of the c-function at the UV fixed point matches with the
Weyl anomaly coefficient (up to an irrelevant factor). The constructed
c-function is the same as one that follows from the "naive limit", which is
obtained by scaling the couplings by a factor of $\frac{1}{D-3}$, and then
setting $D=3$.
