  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 H0, 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 (MOLET) software package is available at:
\url{https://github.com/gvernard/molet}
