  Causal Dynamical Triangulations (CDT) is a non-perturbative quantisation of
general relativity. Ho\v{r}ava-Lifshitz gravity on the other hand modifies
general relativity to allow for perturbative quan- tisation. Past work has
given rise to the speculation that Ho\v{r}ava-Lifshitz gravity might correspond
to the continuum limit of CDT. In this paper we add another piece to this
puzzle by applying the CDT quantisation prescription directly to
Ho\v{r}ava-Lifshitz gravity in 2 dimensions. We derive the continuum
Hamiltonian and we show that it matches exactly the Hamiltonian one derives
from canonically quantising the Ho\v{r}ava-Lifshitz action. Unlike the standard
CDT case, here the intro- duction of a foliated lattice does not impose further
restriction on the configuration space and, as a result, lattice quantisation
does not leave any imprint on continuum physics as expected.
