Using a first-principles pseudopotential approach we study the origin of superconductivity in lithium under pressure. A recently developed Wannier interpolation based technique that allows for ultradense sampling of electron-phonon parameters throughout the Brillouin zone was employed. The electron-phonon coupling strength as a function of pressure was calculated, precisely resolving many of the fine features of its distribution. The contributions to coupling arising from the Fermi surface topology, phonon dispersions, and electronphonon matrix elements were separately analyzed. It is found that of the constituent components, the electronphonon matrix elements are the most sensitive to pressure changes, and a particular phonon is responsible for high values of coupling. Additionally, the distribution of matrix elements over the Fermi surface is seen to be non-uniform and possesses a two-peak structure. Analysis of the Eliashberg spectral function ␣ 2 F͑͒ shows a considerable increase in spectral weight in the low-frequency region with the application of pressure. We estimate the superconducting transition temperature and find that the obtained values are in good accord with experiment.