The unbounded center-of-mass (CM) energy of oppositely moving colliding particles near horizon emerges also in 1+1-dimensional Horava-Lifshitz gravity. This theory has imprints of renormalizable quantum gravity characteristics in accordance with the method of simple power counting. Surprisingly the result obtained is not valid for a 1-dimensional Compton-like process between an outgoing photon and an infalling massless/massive particle. It is possible to achieve unbounded CM energy due to collision between infalling photons and particles. The source of outgoing particles may be attributed to an explosive process just outside the horizon for a black hole and the naturally repulsive character for the case of a naked singularity. It is found that absence of angular momenta in 1+1-dimension does not yield unbounded energy for collisions in the vicinity of naked singularities.