  We provide a theory for quantum-optical realizations of the open Dicke model
with internal, atomic spin states subject to spontaneous emission with rate
$\gamma$. This introduces a second decay channel for excitations to
irreversibly dissipate into the environment, in addition to the photon loss
with rate $\kappa$, which is composed of individual atomic decay processes and
a collective atomic decay mechanism. The strength of the latter is determined
by the cavity geometry. We compute the mean-field non-equilibrium steady states
for spin and photon observables in the long-time limit, $t\rightarrow \infty$.
Although $\gamma$ does not conserve the total angular momentum of the spin
array, we argue that our solution is exact in the thermodynamic limit, for the
number of atoms $N\rightarrow \infty$. In light of recent and upcoming
experiments realizing superradiant phase transitions using internal atomic
states with pinned atoms in optical lattices, our work lays the foundation for
the pursuit of a new class of open quantum magnets coupled to quantum light.
