  In this note we present a sufficient condition ensuring lower semicontinuity
for nonlocal supremal functionals of the type $$W^{1,\infty}(\Omega;\mathbb
R^d)\ni u \mapsto \sup{\rm ess}_{(x,y)\in \Omega} W(x,y, \nabla u(x),\nabla
u(y)),$$ where $\Omega$ is a bounded open subset of $\mathbb R^N$ and $W:\Omega
\times \Omega \times \mathbb R^{d \times N}\times \mathbb R^{d \times N} \to
\mathbb R$.
