  In a recent paper, Grau et al. (2017) studied the zero divisor graphs of the
ring of Lipschitz integers modulo $n$, and computed the domination number of
the undirected zero divisor graph of the ring of Lipschitz integers modulo $n$.
But the case $n$ is a power of prime numbers remained open. In this note, this
problem is solved. We also show the automorphism group of the zero divisor
graph of the ring of Lipschitz integers modulo $2^s$.
