On the basis of density functional theory calculations, we first present a comparative study on the behavior of Li atoms in M (M = Si, Ge, and Sn) and evaluate how Li incorporation affects the electronic structure and bonding nature of the host lattices. We then discuss the energetics, structural evolution, and variations in electronic and mechanical properties of crystalline and amorphous Li-M alloys. Our calculations show that Li insertion is the least favorable in Si and the most favorable in Sn owing to its large effective interstitial space and softer matrix. Upon Li incorporation, the bonding strength of the host network is weakened, attributed to the transferred charge from Li. Li interstitials can migrate easily in all three host materials with a moderate migration barrier in Si and small barriers in Ge and Sn. Because of the cation repulsive interaction, Li atoms tend to remain isolated and well dispersed in M; also induced by this cationic nature is the charge redistribution toward Li, leading to the strong screening/shielding effect in Si, in which the excess charges are highly localized, and a relatively weaker effect in Sn. According to our mixing enthalpy calculations, alloying between Li and M is energetically favorable with Li-Sn alloys being the most stable, followed by Li-Ge and Li-Si alloys. On the basis of structural, electronic, and mechanical property analyses, we also demonstrate how the incorporation of Li atoms with increasing concentration leads to the disintegration of host networks and softening of the Li-M alloys, and associated with the more flexible lattices, the volume expansion at fully lithiated states are 434 (399)% (Si), 382 (353)% (Ge), and 305 (259)% (Sn) for amorphous (crystalline) Li-M alloys.