POLAC (Paris Observatory Lunar Analysis Center) is an ILRS analysis center founded by J. Chapront, M. Chapront-Touzé and G. Francou in 1996. They developed in the 80's a semi-analytical solution of the lunar motion named ELP (Ephémérides lunaires Parisienne). Thus, the original purpose of POLAC was the adjustment of ELP to the lunar laser ranging observations (LLR) for improving the determination of fundamental astronomical parameters, such as the free modes of lunar physical librations, the tidal secular acceleration of the lunar longitude, or the transformation between celestial reference systems. Since the beginning, POLAC worked in close collaboration with the laser ranging station of Grasse (MéO) by providing a posteriori validation of their LLR normal points in order to avoid calibration and format issues. <P />Since 2010 POLAC has evolved. Firstly, it additionally provides predictions for laser ranging observations - mainly for the Moon tracking but also, in an experimental mode, for two ways LRO (Lunar Reconnaissance Orbiter) tracking . The POLAC LLR predictions, originally dedicated and optimized for MéO station, are now the official ILRS prediction for LLR. Secondly, with the elaboration of a new lunar ephemeris called ELPN (Ephéméride lunaire Parisienne Numérique), POLAC also takes part to the long legacy of testing fundamental Physics with laser ranges to the Moon. Indeed, even if ELPN was built originally in the General Relativity (GR) framework, it allows for GR alternative theories of gravity as well. One of particular interest is the Standard Model Extension (SME) which parametrizes Lorentz symmetry violations, notably in the pure gravity sector and in the matter sector of the formalism. By fitting ELPN in the SME framework to the 50 years of collected data, we have been able to provide stringent and realistic estimates on possible Lorentz symmetry violations arising at the level of the weak and the strong Einstein equivalence principles.