Micro-Raman measurements under hydrostatic pressures up to 6GPa have been carried out on high-quality La2-xSrxCuO4 polycrystalline compounds with Sr concentration up to x=0.45. The zz scattering polarization has been investigated, where two strong modes due to La/Sr and the apex oxygen, and (in the low Sr concentrations) the soft mode at ≃100cm-1 are observed. The frequency of the strong modes increases almost linearly with pressure for the Sr concentrations studied. Modifications in the increment rate dω/dp and the phonon width have been detected depending on the amount of doping. For x=0.45 a considerable increase in the width of both strong phonons with pressure was found, which must reflect a separation into phases, since this concentration is close to the solubility limit. The relative intensity of the strong phonons was investigated in connection with its correlation to the transition temperature.