  We analyze the dynamics of an active tracer particle embedded in a thermal
lattice gas. All particles are subject to exclusion up to third nearest
neighbors on the square lattice, which leads to slow dynamics at high
densities. For the case with no rotational diffusion of the tracer, we derive
an analytical expression for the resulting drift velocity v of the tracer in
terms of non-equilibrium density correlations involving the tracer particle and
its neighbors, which we verify using numerical simulations. We show that the
properties of the passive system alone do not adequately describe even this
simple system of a single non-rotating active tracer. For large activity and
low density, we develop an approximation for v. For the case where the tracer
undergoes rotational diffusion independent of its neighbors, we relate its
diffusion coefficient to the thermal diffusion coefficient and v. Finally we
study dynamics where the rotation of the tracer is limited by the presence of
neighboring particles. We find that the effect of this rotational locking may
be quantitatively described in terms of a reduction of the rotation rate.
