The phase diagram LiBH4-ABH4 (A = Rb,Cs) has been screened and revealed ten new compounds LiiAj(BH4)i+j (A = Rb, Cs), with i, j ranging between 1 and 3, representing eight new structure types amongst homoleptic borohydrides. An approach based on synchrotron X-ray powder diffraction to solve crystal structures and solid-state first principles calculations to refine atomic positions allows characterizing multi-phase ball-milled samples. The Li-BH4 substructure adopts various topologies as a function of the compound's Li content, ranging from one-dimensional isolated chains to three-dimensional networks. It is revealed that the Li+ ion has potential as a surprisingly versatile cation participating in framework building with the tetrahydroborate anion BH4 as a linker, if the framework is stabilized by large electropositive counter-cations. This utility can be of interest when designing novel hydridic frameworks based on alkaline metals and will be of use when exploring the structural and coordination chemistry of light-metal systems otherwise subject to eutectic melting.