The crystal structures of two members of the Li2O-B2O3 phase diagram, Li6B4O9 and Li3B11O18, have been solved from single-crystal X-ray diffraction, and their structure has been further confirmed by Rietveld refinement on powder samples. Li613409 crystallizes in the P2(1)/n space group with a = 3.31913(15) angstrom, b = 23.361(2) angstrom, c = 9.1582(4) angstrom, and beta = 92.650(4)degrees. It is the only lithium borate being built upon clusters made of four B03 triangular units linked by vertices. Li3B11O18 adopts also a monoclinic symmetry with a = 17.7607(8) angstrom, b = 7.7737(4) angstrom, c = 9.6731(4) angstrom, and beta = 100.906(4)degrees (space group P2(1)/c); it contains 73% BO3 triangular units and 27% B04 tetrahedra, linked by vertices such that it forms a 3D network containing B3O7 and B5O10 rings. These two new structures and their specificities are discussed in the framework of the dimensional reduction formalism together with other reported lithium borates and may serve as a crystalline reference to study borate glasses.