  The motion of a neutral particle in the vicinity of a slowly rotating black
hole in the Horava-Lifshitz theory of gravity and 3+1 dimensional topological
Lifshitz black hole is investigated. Geodesics for radial motion of the
particles are also plotted. Some different cases of the orbital motion of the
particle are discussed where maximum and minimum values of the effective
potential are calculated. Further the Ba\~{n}ados, Silk and West (BSW)
mechanism is studied for these black holes. It is shown that the centre-of-mass
energy (CME) of two colliding uncharged particles at the horizon of these black
holes remains finite. Thus the BSW effect cannot be seen in these cases.
