  Spin precession in magnetic materials is commonly modelled with the classical
phenomenological Landau-Lifshitz-Gilbert (LLG) equation. Based on a quantized
spin+environment Hamiltonian, we here derive a general spin operator equation
of motion that describes three-dimensional precession and damping and
consistently accounts for effects arising from memory, coloured noise and
quantum statistics. The LLG equation is recovered as its classical, Ohmic
approximation. We further introduce resonant Lorentzian system--reservoir
couplings that allow a systematic comparison of dynamics between Ohmic and
non--Ohmic regimes. Finally, we simulate the full non-Markovian dynamics of a
spin in the semi--classical limit. At low temperatures, our numerical results
demonstrate a characteristic reduction and flattening of the steady state spin
alignment with an external field, caused by the quantum statistics of the
environment. The results provide a powerful framework to explore general
three-dimensional dissipation in quantum thermodynamics.
