  We study the relationship between the pseudogap and Fermi-surface topology in
the two-dimensional Hubbard model by means of the cellular dynamical mean-field
theory. We find two possible mean-field metallic solutions on a broad range of
interaction, doping and frustration: a conventional renormalized metal and an
unconventional pseudogap metal. At half-filling, the conventional metal is more
stable and displays an interaction-driven Mott metal-insulator transition.
However, for large interaction and small doping, region that is relevant for
cuprates, the pseudogap phase becomes the ground state. By increasing doping,
we show that a first-order transition from the pseudogap to the conventional
metal is tight to a change of the Fermi surface from hole to electron like,
unveiling a correlation-driven mechanism for a Lifshitz transition. This
explains the puzzling link between pseudogap phase and Fermi surface topology
which has been pointed out in recent experiments.
