  A lattice regularization for the $2$d projectable Horava-Lifshitz (HL)
quantum gravity is known to be the $2$d causal dynamical triangulations (CDT),
and the $2$d CDT can be generalized so as to include all possible genus
contributions non-perturbatively. We show that in the context of HL gravity,
effects coming from such a non-perturbative sum over topologies can be
successfully taken into account, if we quantize the $2$d projectable HL gravity
with a simple bi-local wormhole interaction. This conference paper is based on
the article, Phys. Lett. B 816 (2021), 136205.
