Single crystals of new Cu,Lu(Ho)–alumoborate and known Cu,Al–borate were synthesized through reaction between CuB2O4 and LnBO3 on the Al2O3 surface by annealing at 1100 °C. Structure of commensurate modification of Ln4AlCu2B9O23, (Ln = Lu,Ho), sp. gr. $P{\bar 4}2_{1}m$, was solved at room temperature. It was found that a low–temperature (110 K) modification possesses incommensurate modulations with modulation vector q =(0, 0, 0.132). The nonaborate block – [B9O23]19– – 9[6T+3Δ] forms an isolated unique dense closed anionic unit. This block is terminated by Al–tetrahedrons in the chessboard pattern, resulting in formation of complex alumoborate layer [AlB9O23]16–. Apical oxygen of central BO3 triangle of the nonaborate block seems to be the source of modulations observed in low temperature polymorph. Cationic layers with the Ln and Cu atoms are alternating along c axis with anionic layers. The structure Cu2Al6B4O17, previously studied by the Rietveld method, was corroborated by single crystal data and was compared with LiAl7B4O17.