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There is a growing interest in the use of legacy terrestrial Global Positioning System (GPS) signals to determine the precise positioning and timing onboard a lunar satellite. Unlike prior works that utilize pseudoranges with meter-level accuracy, we propose a precise positioning and timekeeping technique that leverages carrier-phase measurements with millimeter-level accuracy (when integer ambiguities are correctly fixed). We design an extended Kalman filter framework that harnesses the intermittently available terrestrial GPS time-differenced carrier-phase (TDCP) values and gravitational accelerations predicted by the orbital filter. To estimate the process noise covariance, we implement an adaptive state noise compensation algorithm that adapts to the challenging lunar environment with weak gravity and strong third-body perturbations. Additionally, we perform measurement residual analysis to discard TDCP …