  A new class of laser, which harnesses coherence in both light and atoms, is
possible with the use of ultra-cold alkaline earth atoms trapped in an optical
lattice inside an optical cavity. Different lasing regimes, including
superradiance, superradiant and conventional lasing, are distinguished by the
relative coherence stored in the atoms and in the cavity mode. We analyze the
physics in two different experimentally achievable regions of the superradiant
lasing regime. Our calculations confirm the narrow linewidth of superradiant
lasing for the doubly forbidden clock transition ${}^3 P_0 \to {}^1 S_0$ of
strontium-87 atoms. Under strong driving of the dipole-forbidden transition
${}^3 P_1 \to {}^1 S_0$ of strontium-88 atoms the superradiant linewidth
narrows further due to the coherent excitation of the cavity field.
