  The regime of strong light-matter coupling is typically associated with weak
excitation. With current realizations of cavity-QED systems, strong coupling
may persevere even at elevated excitation levels sufficient to cross the
threshold to lasing. In the presence of stimulated emission, the vacuum-Rabi
doublet in the emission spectrum is modified and the established criterion for
strong coupling no longer applies. We provide a generalized criterion for
strong coupling and the corresponding emission spectrum, which includes the
influence of higher Jaynes-Cummings states. The applicability is demonstrated
in a theory-experiment comparison of a few-emitter quantum-dot--micropillar
laser as a particular realization of the driven dissipative Jaynes-Cummings
model. Furthermore, we address the question if and for which parameters true
single-emitter lasing can be achieved, and provide evidence for the coexistence
of strong coupling and lasing in our system in the presence of background
emitter contributions.
