We present a non-Markovian theory of muon spin relaxation that treats the implanted muon as an open quantum spin coupled to a temporally correlated local magnetic environment. Using a Schwinger-Keldysh influence-functional formulation, we derive a stochastic equation of motion for the muon spin in which the fluctuation kernel is fixed by the local-field correlation tensor, while the retarded memory torque describes an effective environmental backaction. This formulation extends conventional Markovian and strong-collision descriptions to complex magnetic environments where quasistatic broadening, ion-driven colored field fluctuations, and unresolved retarded environmental response coexist and cannot be reduced to a single local-field renewal process. Within the established limits, the theory reduces to standard Kubo-Toyabe forms. This unified framework enables quantitative global analysis of zero-field and weak longitudinal-field $\mu \mathrm{SR}$ spectra, providing a consistent description of field-dependent line shapes with single parameter set at each temperature. Applied to ${\mathrm{Li}}_{0.73}{\mathrm{CoO}}_2$, the model captures the interplay between quenched Gaussian width and a Li-driven dynamical component yielding fluctuation rates consistent with activated behavior. The fitted memory parameter is most visible in the crossover between quasistatic and fast-fluctuation limits, providing a systematic basis for modeling ion-driven magnetic fluctuations in functional materials.

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• Bosons
• Nonequilibrium statistical mechanics
• Open quantum systems
• Spin dynamics
• Spin-phonon coupling
• Lithium-ion batteries
• Muon spin relaxation & rotation
• Non-Markovian processes
• Nonequilibrium Green's function
• Stochastic differential equations