The origin of enhanced superconductivity over 50 K in the recently discovered FeSe monolayer films grown on SrTiO3 (STO), as compared to 8 K in bulk FeSe, is intensely debated. As with the ferrochalcogenides AxFe2-ySe2 and potassium-doped FeSe, which also have a relatively high-superconducting critical temperature (Tc), the Fermi surface (FS) of the FeSe/STO monolayer films is free of hole-like FS, suggesting that a Lifshitz transition by which these hole FSs vanish may help increasing Tc. However, the fundamental reasons explaining this increase of Tc remain unclear. Here we report a 15 K jump of Tc accompanying a second Lifshitz transition characterized by the emergence of an electron pocket at the Brillouin zone centre, which is triggered by high-electron doping following in situ deposition of potassium on FeSe/STO monolayer films. Our results suggest that the pairing interactions are orbital dependent in generating enhanced superconductivity in FeSe.