  We study the relaxation dynamics of a binary Lennard-Jones liquid in the
presence of an amorphous wall generated from equilibrium particle
configurations. In qualitative agreement with the results presented in Nature
Phys. {\bf 8}, 164 (2012) for a liquid of harmonic spheres, we find that our
binary mixture shows a saturation of the dynamical length scale close to the
mode-coupling temperature $T_c$. Furthermore we show that, due to the broken
symmetry imposed by the wall, signatures of an additional change in dynamics
become apparent at a temperature well above $T_c$. We provide evidence that
this modification in the relaxation dynamics occurs at a recently proposed
dynamical crossover temperature $T_s > T_c$, which is related to the breakdown
of the Stokes-Einstein relation. We find that this dynamical crossover at $T_s$
is also observed for a system of harmonic spheres as well as a WCA liquid,
showing that it may be a general feature of glass-forming systems.
