In this paper, we develop a general framework for simulating Lindblad-type dynamics with a wavefunction description. As opposed to the SSE approaches that stochastically change both the magnitudes and the phases of the quantum expansion coefficients, our new method only stochastically changes the phases of the expansion coefficients, and exactly reproduces the jump operator dynamics of the Lindblad master equation. In particular, we give the derivation of a method to propagate the coefficients of the MFE method that fully agrees with Lindblad dynamics. The coefficient-propagation method derived using this framework is inspired by the Ehrenfest+R method; however, our approach exactly recovers Lindblad dynamics whereas the Ehren-fest+R approach does not. Additionally, we derive a simple fix to the approximations present in the Ehren-fest+R method and give rigorous justifications for particular algorithmic choices. Our wavefunction description of Lindblad dynamics can be seamlessly integrated into mixed quantum-classical methods that simulate coupled electronic-nuclear dynamics, such as the mean-field Ehrenfest approach, and we refer to this particular approach as the L-MFE method. We have tested the accuracy, efficiency, and robustness of the L-MFE method through numerical simulations. We envision that our work will provide a general framework for future theoretical work into incorporating Lindblad dynamics into more accurate semiclassical and mixed quantum-classical approaches.