Quenching mechanisms of the Li3p and Li4p states in collision with the nitrogen molecule are studied by laser-induced fluorescence spectroscopy and by a quantum chemical calculation. The Li3p state is observed to be efficiently quenched to the Li3s state detected as intense 3s-->2p emission. The Li4p state is efficiently quenched to the Li4s and Li3d states detected as 4s-2p and 3d-2p emissions, respectively. The potential-energy surfaces for the Li(2s-4p)N2 states show a large number of conical intersections and avoided crossings resulting from the couplings between the ionic [Li+(N2)-] and covalent configurations. There are a large number of stable excited states, and we give here the spectroscopic constants for the lowest two stable isomers correlating to Li2p+N2.