We present the time-resolved spectral analysis of the XMM-Newton data of NGC 1365 collected during one XMM-Newton observation, which caught this "changing-look" active galactic nucleus in a high flux state characterized also by a low column density (N H ~ 1022 cm-2) of the X-ray absorber. During this observation, the low-energy photoelectric cut-off is at about ~1 keV and the primary continuum can be investigated with the XMM-Newton-RGS data, which show strong spectral variability that can be explained as a variable low N H that decreased from N H ~ 1023 cm-2 to 1022 cm-2 in a 100 ks timescale. The spectral analysis of the last segment of the observation revealed the presence of several absorption features that can be associated with an ionized (log ξ ~ 2 erg cm s-1) outflowing wind (v out ~ 2000 km s-1). We detected for the first time a possible P-Cygni profile of the Mg XII Lyα line associated with this mildly ionized absorber indicative of a wide angle outflowing wind. We suggest that this wind is a low ionization zone of the highly ionized wind present in NGC 1365, which is responsible for the iron K absorption lines and is located within the variable X-ray absorber. At the end of the observation, we detected a strong absorption line at E ~ 0.76 keV most likely associated with a lower ionization zone of the absorber (log ξ ~ 0.2 erg cm s-1, N H ~ 1022 cm-2), which suggests that the variable absorber in NGC 1365 could be a low ionization zone of the disk wind.