In previous work, we have developed an autoregressive Mixed-Effects model of the evolution of the kinetic gene expression parameters along cell generations, and an identification method simultaneously exploiting single-cell gene expression profiles and known parental relationships among cells (lineage tree data). Here, we extend our modelling and identification approach to explicitly account for stochasticity of promoter activation, and demonstrate via simulation the performance of the method and the improvement relative to the original approach where this source of noise is not accounted for.