Landscape Evolution Models (LEMs) are prime tools to simulate the evolution of source-to-sink systems through ranges of spatial and temporal scales. Plethora of different empirical laws have been successfully applied to describe the different parts of these systems: fluvial erosion, sediment transport and deposition, hillslope diffusion, or hydrology. Numerical frameworks exist to facilitate the combination of different subsets of laws, mostly by superposing grids of fluxes calculated independently. However the exercise becomes increasingly challenging when the different laws are inter-connected: for example when a lake breaks the upstream-downstream continuum of the amount of sediment and water it receives and transmits; or when erosional efficiency depends of the composition of a sediment flux affected by multiple processes. In this contribution, we present a method mixing the advantages of cellular-automata and graph theory to address such cases. We demonstrate how the former guarantees finite knowledge of all fluxes independently from the process-law implemented in the model while the latter offer a wide range of tools to process numerical landscapes, including landscapes with closed basins. We provide three scenario largely benefiting from our method: i) one where lake systems are primary controls on Landscape evolution, ii) one where sediment provenance is closely monitored through the stratigraphy and iii) one where heterogeneous provenance influences fluvial incision dynamically. We finally outline the way forward to make this method more generic and flexible.