The direct collisional energy transfer process Li*(3p) + CH4 --> Li*(3s) + CH4 is investigated both theoretically and experimentally. We measured the nonreactive far-wing absorption profiles of the LiCH4 complexes by monitoring the Li(3s) --> Li(2p) fluorescence at 812.6 nm. The intensity of the Li(3s) --> Li(2p) fluorescence decreases with detuning, indicating a more efficient transition rate at low detuning. A high level ab initio calculation in both C-2nu and C-3nu symmetry is performed to provide a general picture of the nonradiative transition induced by collisions between lithium atoms and a methane molecule.