We demonstrate a novel method to manipulate the Fermi level around the Van Hove singularity (VHS) in Li-intercalated graphene on the SiC single crystal. By angle-resolved photoemission spectroscopy, we observed a Lifshitz transition around the VHS when the thickness of graphene exceeds four layers. We calculated the band structure of a multilayer system with different stacking sequences of graphene and Li layer. The so-called stage 2 model reproduces the Lifshitz transition, where Li occupies every other interlayer of graphene. These properties allow us to explore the electronic phase diagram around the VHS by tuning the thickness.