We present an analytical model for the evolution of extended active galactic nuclei (AGNs) throughout their full lifecycle, including the initial jet expansion, lobe formation, and eventual remnant phases. A particular focus of our contribution is on the early jet expansion phase, which is traditionally not well captured in analytical models. We implement this model within the Radio AGN in Semi-Analytic Environments (RAiSE) framework, and find that the predicted radio source dynamics are in good agreement with hydrodynamic simulations of both low-powered Fanaroff-Riley Type-I and high-powered Type-II radio lobes. We construct synthetic synchrotron surface brightness images by complementing the original RAiSE model with the magnetic field and shock-acceleration histories of a set of Lagrangian tracer particles taken from an existing hydrodynamic simulation. We show that a single set of particles is sufficient for an accurate description of the dynamics and observable features of Fanaroff-Riley Type-II radio lobes with very different jet parameters and ambient density profile normalizations. Our new model predicts that the lobes of young (≲10 Myr) sources will be both longer and brighter than expected at the same age from existing analytical models, which lack a jet-dominated expansion phase; this finding has important implications for interpretation of radio galaxy observations. The RAiSE code, written in python, is publicly available on github and pypi.