The Laser Ranged Satellites Experiment (LARASE) aims to test the gravitational interaction in the weak-field and slow-motion limit and compare, consequently, the predictions of Einstein’s theory of general relativity (GR) with those of other alternative theories of gravitation. In particular, a goal of LARASE is to improve the modelling of the non-gravitational perturbations (NGP) on the LAGEOS, LAGEOS II and LARES satellites in such a way to further improve their precise orbit determination in order to better extract, from their orbital residuals, the expected tiny relativistic effects. Indeed, the motion of these passive laser-ranged satellites along nearly geodesics of spacetime may be a posteriori reconstructed through a careful modelling of the main NGP that act on their surface and, in more general terms, of their overall dynamical models. We will focus upon two recent LARASE results: the development of a new model for the spin evolution of the satellites and of one to account for the very subtle effects on their orbits that are produced by the thermal thrust perturbations. Concerning the gravitational perturbations due to the deviation of the Earth's mass distribution from that of a perfect sphere, we will discuss our improvements in the modelling of the Earth's even zonal harmonics coefficients based on GRACE data, specifically in their time-dependency. Finally, we will show our new results for a refined measurement of the Lense-Thirring precession on the combined orbits of the LAGEOS, LAGEOS II and LARES satellites. This relativistic precession arises from the gravitomagnetic field of the Earth produced by its angular momentum. Gravitomagnetism describes, in Einstein’s GR, the curvature of spacetime produced by mass-currents, with important consequences in the astrophysics of high-energy phenomena as well as possible cosmological consequences related to Mach’s Principle.