  We study the dynamics of a particle moving in a square two-dimensional
Lorentz lattice-gas. The underlying lattice-gas is occupied by two kinds of
rotators, "right-rotator (R)" and "left-rotator (L)" and some of the sites are
empty {\it{viz.}} vacancy "V".The density of $R$ and $L$ are the same and
density of $V$ is one of the key parameters of our model. The rotators
deterministically rotate the direction of a particle's velocity to the right or
left and vacancies leave it unchanged. We characterise the dynamics of particle
motion for different densities of vacancies. Since the system is deterministic,
the particle forms a closed trajectory asymptotically. The probability of the
particle being in a closed or open trajectory at time $t$ is a function of the
density of vacancies. \textcolor{black}{The motion of the particle is
{\it{uniform}} throughout in a fully occupied lattice. However, it is divided
in two distinct phases in partially vacant lattices}: The first phase of the
motion, which is the focus of this study, is characterised by anomalous
diffusion and a power-law decay of the probability of being in an open
trajectory. The second phase of the motion is characterised by subdiffusive
motion and an exponential decay of the probability of being in an open
trajectory. For lattices with a non-zero density of vacancies, the first phase
of motion lasts for a longer period of time as the density of vacancies
increases.
