Using density functional theory (DFT), the structures, stability, chemical bonding and aromaticity of lanthanide complexes bearing the derivatives of 1-borabicyclo$$1.1.0$$but-2(3)-ene (1BB) and 2-borabicyclo$$1.1.0$$but-1(3)-ene (2BB), (bis-1BB)LnCl3 and (bis-2BB)LnCl3 (Ln=Sc, Y, La, Nd, Sm, Dy, Ho, Yb and Lu), have been investigated. Calculated results indicate that bis-1BB and bis-2BB can coordinate with LnCl3 to form stable lanthanide complexes. The lengths of Ln—C and Ln—N bonds in (bis-1BB)LnCl3 and (bis-2BB)LnCl3, as well as the electron density and Laplacian values of Ln—C and Ln—N bonds in (bis-1BB)LnCl3 and (bis-2BB)LnCl3 show that Ln—C and Ln—N have covalent bond characteristic, in which the distances of Ln—C and Ln—N bonds in (bis-1BB)LnCl3 and (bis-2BB)LnCl3 (Ln=Sc, Y, La, Sm and Lu) are close to those of in (bis-NHC)LnCl3. Thus, the bis-1BB and bis-2BB are analogous to the well-established bis-NHC. The NICS(0) values in the centers of the three- and six-membered rings of these lanthanide complexes show that the three- and six-membered rings have strong aromaticity. In particular, (bis-1BB)LnCl3 and (bis-2BB)LnCl3 complexes are thermodynamically favorable to be formed and contain two planar tetracoordinate carbons (ptCs). Thus, a family of novel stable lanthanide complexes with ptC is theoretically obtained.