In the context of the relaxation time approximation to Boltzmann transport theory, we examine the behavior of the Hall number nH of a metal in the neighborhood of a Lifshitz transition from a closed Fermi surface to open sheets. We find a universal nonanalytic dependence of nH on the electron density in the high-field limit, but a nonsingular dependence at low fields. The existence of an assumed nematic transition produces a doping dependent nH similar to that observed in recent experiments in the high-temperature superconductor YBa2Cu3O7-x. © 2017 American Physical Society.