Recent lightwave-STM experiments have shown space and time resolution of single molecule vibrations directly on their intrinsic length and timescales. We address here theoretically the electronic dynamics of a copper-phthalocyanine in a lightwave-STM explored within a pump-probe cycle scheme. The spin-orbit interaction in the metallic center induces beatings of the electric charge flowing through the molecule as a function of the delay time between the pump and the probe pulses. Interference between the quasidegenerate anionic states of the molecule and the intertwined dynamics of the associated spin and pseudospin degrees of freedom are the key aspects of such phenomenon. We study the dynamics directly in the time domain within a generalized master-equation approach.