  In this paper we address the issue of black hole solutions in
(1+1)-dimensional non-projectable Horava-Lifshitz gravity. We consider several
models by considering different potentials in the scalar matter sector. We also
consider the gravitational collapse of a distribution of pressureless dust
filling a region in one-dimensional space. The time of the collapse can be
faster or slower depending on the parameter $\lambda$ of the theory.
