  We present the simulation of a $2\times10^9 M_\odot$ halo mass cosmological
dwarf galaxy run to $z=0$ at 4 solar mass gas resolution with resolved
supernova feedback. We compare three simple subgrid implementations for the
inhomogeneous chemical enrichment from Population III stars and compare them to
constraints from Local Group dwarf galaxies. The employed model, LYRA, is a
novel high resolution galaxy formation model built for the moving mesh code
AREPO, which is marked by a resolved multi-phase interstellar medium, single
stars and individual supernova events. The resulting reionization relic is
characterized by a short ($<1.5$ Gyr) star formation history that is repeatedly
brought to a standstill by violent bursts of feedback. Star formation is
reignited for a short duration due to a merger at $z\approx4$ and then again at
$z\approx0.2-0$ after sustained gas accretion. Our model $z=0$ galaxy matches
the stellar mass, size, stellar kinematics and metallicity relations of Local
Group dwarf galaxies well. The dark matter profile does not exhibit a core in
any version of the model. We show that the host halo masses of Population III
stars affect the assembly history of dwarf galaxies. This manifests itself
through the initial gaseous collapse in the progenitor halos, affecting the
central density of the stellar component and through the accretion of luminous
substructure.
