We present a self-consistent and versatile forward modelling software package that can produce time series and pixel-level simulations of time-varying strongly lensed systems. The time dimension, which needs to take into account different physical mechanisms for variability such as microlensing, has been missing from existing approaches and it is of direct relevance to time delay, and consequently H-0, measurements and caustic crossing event predictions. Such experiments are becoming more streamlined, especially with the advent of time domain surveys, and understanding their systematic and statistical uncertainties in a model-aware and physics-driven way can help improve their accuracy and precision. Here, we demonstrate the software's capabilities by exploring the effect of measuring time delays from lensed quasars and supernovae in many wavelengths and under different microlensing and intrinsic variability assumptions. In this initial application, we find that the cadence of the observations and combining information from different wavelengths plays an important role in the correct recovery of the time delays. The mock lenses in time software package is available at https://github.com/gvernard/molet.