Structures and energies of the binary B2Lin (n = 1-4) clusters are predicted with the HF, MP2, and B3LYP methods using the 6-31G(d) basis set, including energy evaluations at G2MP2 and CBS-Q and the larger 6-311+G(2d) basis set for B3LYP. All systems except B2Li4 are also computed with the CASSCF method because of spin contamination for several of the open-shell systems. These were followed by energy evaluations with multiconfigurational perturbation theory. The global B2Li minimum has a C-2v triangular form of which the B-2(1) State is 13 kcal/mol more stable than the (2)A(1) state. A bent double Li-bridged structure (C-2v) is the global B2Li2 minimum with a 2.0 kcal/mol inversion barrier. The global minimum for B2Li3 is a triple Li-bridged propellane-like structure (D-3h), and for B2Li4 it is the quadruple Li-bridged structure (D-4h). All these structure have a high degree of ionicity, but in B2Li4 stabilization through LiLi interactions also become important. Structural patterns for the isomers of these clusters are examined. Cohesive energies (B2Lin --> B-2 + Li-n) and Li and Li-2 elimination energies are analyzed in terms of cluster stabilities.