Lithium is one of the simplest metals, with negative charge carriers and a close reproduction of free-electron dispersion. Experimentally, however, Li is one of a handful of elemental solids (along with Cu, Ag, and Au) where the sign of the Seebeck coefficient (S) is opposite to that of the carrier. This counterintuitive behavior still lacks a satisfactory interpretation. We calculate S fully from first principles, within the framework of Allen's formulation of Boltzmann transport theory. Here it is crucial to avoid the constant relaxation time approximation, which gives a sign for S which is necessarily that of the carriers. Our calculated S are in excellent agreement with experimental data, up to the melting point. In comparison with another alkali metal, Na, we demonstrate that within the simplest nontrivial model for the energy dependency of the electron lifetimes, the rapidly increasing density of states (DOS) across the Fermi energy is related to the sign of S in Li. The exceptional energy dependence of the DOS is beyond the free-electron model, as the dispersion is distorted by the Brillouin zone edge; this has a stronger effect in Li than other alkali metals. The electron lifetime dependency on energy is central, but the details of the electron-phonon interaction are found to be less important, contrary to what has been believed for several decades. Band engineering combined with the mechanism exposed here may open the door to new "ambipolar" thermoelectric materials, with a tunable sign for the thermopower even if either n- or p-type doping is impossible.