Lean premixed (LPM) combustors allow reduction of NOx emissions, but they often experience instabilities that are detrimental for engines structural integrity and performances. Most of the works dealing with LPM combustors oscillations address the occurrence of dynamic regimes to system instabilities, i.e., to the coupling between variations of heat release from the flame and acoustic modes of the combustion chamber. However, premixed flames may be prone to intrinsic instabilities: the flame itself oscillates, independently from the coupling with combustor acoustics. In the present article, RANS-based CFD simulations were performed to study the dynamic behavior of an LPM combustor by varying the length of the inlect duct, the inlet gas velocity and fuel equivalence ratio, and the combustor wall temperature. The model results show that the LPM combustor oscillations may be different in nature: they may originate from system instabilities or from the propagation to the whole combustor of the flame intrinsic oscillations due to heat losses (thermo-kinetic oscillations). Furthermore, it is found that whatever the driving mechanism ( system or flame instability) a whole acoustic mode is excited and, accordingly, Rayleigh's criterion is always verified. Conversely, the widely used re-statement of Rayleigh's criterion based on the time-delay approach is verified only for the oscillations originated by system instability, while it fails with the thermo-kinetic oscillations. A way to discern between the different mechanisms exciting the oscillations in an LPM combustor is then suggested.