  We investigate spectral properties of the atomic fluorescence and the output
field of the cavity-mode of a single-atom dressed-state laser in a photonic
crystal. We pay a particular attention to the behavior of the spectra in the
presence of the frequency dependent reservoir and search for signatures of the
thresholdless lasing. Although the thresholdless behavior has been predicted by
analyzing the photon statistics of the cavity field, we find that the threshold
behavior still exists in the spectrum of the cavity field. We find that the
structure of cavity field spectrum depends strongly on the strange of the
pumping rate. For low pumping rates, the spectrum is not monochromatic, it is
composed of a set of discrete lines reveling the discrete (quantum) structure
of the combined dressed-atom plus the cavity field system. We find that for a
certain value of the pumping rate, the multi-peak structure converts into a
single very narrow line centered at the cavity field frequency. A physical
explanation of the behavior of the spectra is provided in terms of dressed
states of the system.
