  The automorphism groups of integral Lorentzian lattices act by isometries on
hyperbolic space with finite covolume. In the case of reflective integral
lattices, the automorphism groups are commensurable to arithmetic hyperbolic
reflection groups. However, for a fixed dimension, there is only finitely many
reflective integral Lorentzian lattices, and these can only occur in small
dimensions. The goal of this note is to construct embeddings of low-dimensional
integral Lorentzian lattices into unimodular Lorentzian lattices associated to
right-angled reflection groups. As an application, we construct many discrete
groups of $\mathrm{Isom}(\mathbb{H}^n)$ for small $n$ which are C-special in
the sense of Haglund-Wise.
