  The atmospheric lepton fluxes play a crucial role in many particle and
astroparticle physics experiments, e.g. in establishing the neutrino signal and
the muon background for neutrino oscillation measurements, or the atmospheric
background for astrophysical neutrino searches. 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 costs. Previously, the
MCEq framework only accommodated longitudinal development of air showers, an
approximation that works well for neutrino and muon fluxes at high energies
(O(10 GeV) and above). However, for accurate calculations of atmospheric lepton
angular distributions at lower energies, the lateral component of hadronic
cascades becomes significant, necessitating three-dimensional calculation
schemes. We introduce "2D MCEq", an efficient numerical approach for combined
longitudinal and angular evolution of air showers that retains the low
computational complexity. The accuracy of the "2D MCEq" is affirmed by its
benchmark comparison with the standard Monte Carlo code CORSIKA. This study
paves the way for efficient three-dimensional calculations of atmospheric
neutrino fluxes.

High Energy Astrophysical Phenomena;High Energy Physics - Phenomenology