The Matrix Cascade Equations (MCEq) code is a numerical tool used to model the atmospheric lepton fluxes by solving a system of coupled differential equations for particle production, interaction, and decay at extremely low computational cost. Previous iterations of the MCEq code relied on a longitudinal-only development of air showers, which was sufficient for modelling neutrino and muon fluxes at energies around 10 GeV and above. However, for precision calculations of atmospheric lepton angular distributions at energies below a few GeV, the lateral component of hadronic cascades becomes important. This study introduces a robust numerical technique for the combined longitudinal and angular evolution of air showers, which retains the low computational cost of the MCEq code. We compare our numerical solutions to those obtained with the standard Monte Carlo code CORSIKA and show that our new "2D MCEq" is sufficiently accurate. This approach enables fast two-dimensional evolution of hadronic cascades in arbitrary media and is an important bridge between the computationally efficient one-dimensional and the three-dimensional lepton flux calculations.