  We derive a BPS-like first order system of equations for a family of flat
static domain walls (DWs) of dimensionally extended cubic Lovelock Gravity
coupled to massive scalar self-interacting matter. The explicit construction of
such DWs is achieved by introducing of an appropriate matter superpotential. We
further analyse the dependence of the geometric properties of the
asymptotically AdSd space-times representing distinct DWs on the shape of the
matter potential, on the values of the Lovelock couplings and on the scalar
field boundary conditions. Few explicit examples of Lovelock DWs interpolating
between AdS-type vacua of different cosmological constants are presented. In
five dimensions our method provides interesting solutions of the Myers-Robinson
Quasi-topological Gravity in the presence of matter important for the
description of the specific renormalization group flows in its holographic dual
four-dimensional CFT perturbed by relevant operators.
