We present in this paper an analysis of our preliminary results for point spread function reconstruction in laser guide star (LGS) mode for the Keck-II adaptive optics system. Our approach is based on an update of the natural guide star algorithm with the LGS terms. The first reconstruction we have done is based on a set of 13 LGS runs (telemetry data and sky PSF) for which we demonstrate already a significant correlation between the reconstructed and sky PSF metrics. At this point of the project, though, our reconstructed PSF does not reproduce the sky PSF features (and this is expected) : we discuss why, and describe the different issues we have to solve, and the different experiment we will do, in order to achieve a good reconstruction.