Lithium forms high-spin clusters, Li-n+1(n) which are bonded even though there are no electron-pairs! This no-pair bonding is weak for the (3)Sigma(u)(+) state of Lit but becomes very significant for larger clusters reaching up to 1.8 eV for Li-7(6). To understand the nature of "no-pair bonding", we performed valence bond (VB) calculations on the states of Li-2, benchmarked them against high-level MO-based calculations which account for static as well as dynamic electron correlation, and derived bonding mechanisms for the no-pair triplet state vis a vis the singlet ground state. It is shown that both the singlet-pair and no-pair bonds are bonded by covalency but differ in the mechanism of VB mixing. The singlet-pair bond is sustained by covalency augmented by Coulomb correlation of the electron pair, while the no-pair bond originates solely in the resonance energy between the repulsive fundamental triplet VB structure with the secondary VB structures. Understanding of the fundamental no-pair bond in Li-3(2) enables one to derive insight into the bonding and geometric features of no-pair Li-n+1(n) high-spin clusters. Experimental characterization of such clusters will broaden the current conception of bonding beyond the traditional spin-pairing paradigm.