Refs. [37, 38] was done in the application region of the proximity force approximation (PFA) [2, 8, 11]. The lateral Casimir force with an amplitude of 3 . 2 × 10 − $^{13}$N at the shortest separation of 221 nm was found to sinusoidally oscillate as a function of the phase shift between the corrugations. The total experimental error of the force amplitude measurement at the closest point was determined to be around 19% at the 95% confidence level [2]. The experimental results were compared with theory using the PFA which should supposedly be applicable at separations much smaller than the corrugation period. In so doing the dielectric properties of Au were described using the simple plasma model in fourth order perturbation theory with respect to a small parameter related to the ratio of the skin depth to the separation distance. The experimental results were found to be in good agreement with the theory in the limits of the experimental error. It was also predicted theoretically (but not observed experimentally due to the use of small corrugation amplitudes and insufficient precision) that the lateral Casimir force is asymmetric, i.e., deviates from purely sinusoidal harmonic dependence on the phase shift, through the contribution of higher order terms in the perturbation expansion with respect to the corrugation amplitudes. In this paper we present complete measurement data of the recently performed experi- ment on the lateral Casimir force between a sinusoidally corrugated sphere and plate covered with Au layers. The much smaller period of corrugations used in this experiment provides opportunities to measure deviations of the lateral Casimir force from the theoretical predic- tions obtained on the basis of the PFA. Much deeper corrugations on both the sphere and the plate and shorter separations where the measurements were performed make it possible to demonstrate the asymmetry of the lateral Casimir force, as predicted in Ref. [38]. The measurement data are compared with the exact theory describing the Rayleigh scattering of the electromagnetic oscillations on the sinusoidally corrugated boundary surfaces of a sphere and a plate with no fitting parameters. Only the configuration of a perfect sphere near a plane plate is treated using the PFA. At the separations considered, this leads to only a negligibly small error of order 0.1% [2, 11]. The dielectric properties of Au are described by means of the generalized plasma-like model [39, 40] which takes into account the interband transitions of core electrons. The computational results for the amplitude of the lateral Casimir force as a function of separation and for the lateral Casimir force as a function of the phase shift at different separations obtained using the exact theory at the laboratory temperature ( T = 300 K) are found to be in a very good agreement with the measurement 5