  We calculate the phase diagram of identical fermions in a 2-dimensional (2D)
lattice immersed in a 3D Bose-Einstein condensate (BEC). The fermions exchange
density fluctuations in the BEC, which gives rise to an attractive induced
interaction. The resulting zero temperature phase diagram exhibits topological
$p_x+ip_y$ superfluid phases as well as a phase separation region. We show how
to use the flexibility of the Bose-Fermi mixture to tune the induced
interaction, so that it maximises the pairing between nearest neighbour sites,
whereas phase separation originating from long range interactions is
suppressed. Finally, we calculate the Berezinskii-Kosterlitz-Thouless (BKT)
critical temperature of the topological superfluid in the lattice and discuss
experimental realisations.
