In this paper we scrutinize the so called Principle of Local Lorentz Invariance (PLLI) that many authors claim to follow from the Equivalence Principle. Using rigourous mathematics, we introduce in the General Theory of Relativity two classes of reference frames (PIRFs and LLRFγs) which as natural generalizations of the concept of the inertial reference frames of the Special Relativity Theory. We show that it is the class of the LLRFγs that is associated with the PLLI. Next we give a definition (...) of physically equivalent reference frames. Then, we prove that there are models of General Relativity Theory (in particular on a Friedmann universe) where the PLLI is false. However our finding is not in contradiction with the many experimental claims vindicating the PLLI, because theses experiments do not have enough accuracy to detect the effect we found. We prove moreover that PIRFs are not physically equivalent. (shrink)