  Open quantum walks (OQWs) describe a quantum walker on an underlying graph
whose dynamics is purely driven by dissipation and decoherence. Mathematically,
they are formulated as completely positive trace preserving (CPTP) maps on the
space of density matrices for the walker on the graph. Any microscopically
derived OQW must include the possibility of remaining on the same site on the
graph when the map is applied. We extend the CPTP map to describe a lazy OQW.
We derive a central limit theorem for lazy OQWs on a $d$-dimensional lattice,
where the distribution converges to a Gaussian. We show that the properties of
this Gaussian computed using conventional methods agree with the general
formulas derived from our central limit theorem.
