A way resulting in lasing without inversion (LWI) in an open resonant Λ-type system from a nonlinear dynamics viewpoint is investigated. The destabilization of the non-lasing solution can occur not only through pitchfork bifurcation, giving rise to continuous wave LWI, but also through Hopf bifurcation, giving rise to self-pulsing LWI. This is much different from that of the corresponding closed resonant Λ-type system in which the destabilization of the non-lasing solution can occur only through pitchfork bifurcation. The effects of the unsaturated gain coefficient, cavity loss coefficient, atomic injection and exit rates on the two bifurcations are discussed.