This paper presents the large Eddy simulation (LES) of a propeller representative of the first rotor of a counter rotative open rotor (CROR) configuration based on a multiple frequency phase-lagged approach in conjunction with a proper orthogonal decomposition (POD) data storage. This method enables to perform unsteady simulations on multistage turbomachinery configurations including multiple frequency flows with a reduction of the computational domain composed of one single blade passage for each row. This approach is advantageous when no circumferential periodicity occurs in the blade rows of the configuration and a full 360 deg simulation would be required. The data storage method is based on a POD decomposition replacing the traditional Fourier series decomposition (FSD). The inherent limitation of phase-shifted periodicity assumption remains with POD data storage but this compression method alleviates some issues associated with the Fourier transform, especially spectrum issues. The paper is first dedicated to compare the flow field obtained with the LES with phase-lagged condition against full-matching URANS, LES simulations, and experimental data available around the blade and in the wake of the rotor. The study shows a close agreement of the phase-lagged LES simulation with other simulations performed and a thicker wake compared with the experiments with lower turbulent activity. The analysis of the losses generated in the configuration, based on an entropy formulation and a splitting between boundary layer and secondary flow structures, shows the strong contribution of the blade boundary layer in the losses generated.