When a Markovian approximation of the systemenvironment interaction is valid, the Lindblad master equation offers the most general and quantum mechanically valid description of an open system's quantum dynamics, as it guarantees the positivity and preserves the trace of the reduced density matrix. Thus, it is ideal to use this computationally efficient and analytically simple Lindblad master equation to describe the influence of those Markovian environmental DOFs on the quantum subsystem, while simultaneously using the MQC approximation to incorporate the influence of the anharmonic, non-Markovian nuclear DOFs on the quantum subsystem. Indeed, the density matrix hybrid method, which is based on this idea, has been developed recently to study non-adiabatic dynamics by combining MQC methods and master equation approaches. Still, solving the Lindblad master equation with many states in the quantum system is computationally challenging, due to the need to propagate the density matrix in the Liouville space.