The phase diagram of correlated systems like cuprate or pnictide high-temperature superconductors is likely defined by a topological change of the Fermi surface under continuous variation of an external parameter, the so-called Lifshitz transition. However, a number of low-temperature instabilities and the interplay of multiple energy scales complicate the study of this phenomenon. Here we identify the optical signatures of a pressure-induced Lifshitz transition in a clean elemental system, black phosphorus. By applying external pressures above 1.5 GPa, we observe a change in the pressure-dependent Drude plasma frequency due to the appearance of massless Dirac fermions. At higher pressures, optical signatures of two structural phase transitions are also identified. Our findings suggest that a key fingerprint of the Lifshitz transition, in the absence of structural transitions, is a Drude plasma frequency discontinuity due to a change in the Fermi surface topology.