In the presented work, the possibility of controlling laser generation using a nematic liquid crystal (NLC) in a hybrid layered structure consisting of a thin metal layer (Ag), a layer of NLC doped with a light-absorbing dye, and a distributed Bragg reflector (DBR) with a rectangular refractive index profile is theoretically studied. Spectral dependencies of the reflection, transmission, and absorption coefficients of light as well as the localization coefficient of the light field in NLC within the photonic bandgap of the DBR are obtained. Narrow dips in the reflection coefficient and peaks in the transmission coefficient are achieved due to the excitation of plasmons at the Ag-NLC interface. The dependence of the spectral position and magnitude of the plasmonic dips/peaks and the enhancement of the light field in the NLC medium on the thickness and orientation of the NLC layer as well as the impact of a light-absorbing dye doping are investigated. Theoretical calculations of the temporal dependencies of luminescence pulses for pumping pulses of different power settings (below, above, and at the threshold of laser generation) and different values of light absorption in the dye-doped NLC medium are performed, taking into account the peculiarities of the optical properties of the dye-doped NLC.