  In this paper, we study the non-projectable 2d Ho\v{r}ava gravity coupled
with a non-relativistic scalar field, where the coupling is in general
non-minimal and of the form $f(\phi)R$, where $f(\phi)$ is an arbitrary
function of the scalar field $\phi$, and $R$ denotes the 2d Ricci scalar. In
particular, we first investigate the Hamiltonian structure, and show that there
are two-first and two-second class constraints, similar to the pure gravity
case, but now the local degree of freedom is one, due to the presence of the
scalar field. Then, we present various exact stationary solutions of this
coupled system, and find that some of them represent black holes but now with
universal horizons as their boundaries. At these horizons, the Hawking
radiations are thermal with temperatures proportional to their surface
gravities, which normally depend on the non-linear dispersion relations of the
particles radiated, similar to the (3+1)-dimensional case.
