This work provides a general approach for incorporating the Markovian dynamics of the Lindblad master equation into a scalable, wavefunction-type approach, allowing for the description of the dynamics of a quantum subsystem interacting with an anharmonic classical subsystem (nuclei) through a mixed quantum-classical description, as well as a Markovian environment that can be accurately described by Lindblad dynamics. The current approach can readily be used in the context of describing spontaneous emission due to light-matter interactions, incorporating cavity leaking in polariton chemistry, or being combined with Ehrenfest dynamics or a surface hopping approach to incorporate decoherence corrections. We envision that the current approach provides a general framework for future work to incorporate Lindblad dynamics into other mixed quantum-classical or semiclassical approaches.