The damage of aircraft outer skin by lightning strike is a complex multi-physics problem and a severe issue in aeronautics. The plasma interacting with the aircraft is a non-stationary and non-optically thin electric arc. Under a 100 kA lightning strike, temperature and pressure up to 40 kK and 20 bars, respectively, are observed in the arc column [1]. Measuring temperature and pressure profile of the arc root is needed to validate numerical simulation of the phenomenon and existing experimental data are seldom in the literature. We propose such measurements in the present study using optical emission spectroscopy and propose a reconstruction method solving the radiation transfer equation to obtain spatial temperature and pressure profiles at different arc lifetimes. We study this interaction on aeronautic aluminium samples 2 mm thick. A 10 cm long pulsed electric arc is generated above the sample. To study the arc root, high speed imaging and optical emission spectroscopy were performed. High speed imaging provides morphology of the arc root and a constriction in the vicinity of the sample is observed. A direct optical setup is developed to obtain emission spectroscopy spectra with an improved spatial resolution compared to previous work. Measurements of temperature and pressure profiles are obtained close to the sample by numerical reconstruction. The reconstruction method based on Spline candidate functions is presented.