We present a dressed-atom theory of a four-level, double-LAMBDA atomic configuration interacting with a strong laser light which induces a superposition of two lower states. The presence of the cavity and of damping is fully taken into account and the conditions and characteristics of a possible lasing without inversion between the unperturbed states are determined analytically. The special case of the Zeeman-degenerate J = 1 lower state is found to be particularly attractive for a possible practical realization.