The paper considers the application of X-ray spectroscopy with high spatial resolution for investigation of magnetic reconnection in laboratory astrophysical experiments carried out on laser facilities of nano- and pico-second duration at moderate laser intensity on the target 1018 W/cm2. A brief overview of commonly used experimental schemes is given. We present atomic kinetic calculations for the spectra from the L-shells of Ne- and F-like iron ions (Fe, Z = 26), which demonstrate the high sensitivity of the spectra to changes in plasma parameters. An analysis of the range of applicability of various diagnostic approaches to assessing the electron temperature and laser plasma density is carried out. It is shown that transition lines in Ne-like ions are a universal tool for measuring plasma parameters, both in the region of laser interaction with the target and in the reconnection zone.