A family of 3D lanthanide metal–organic frameworks, [La(HTADIP)(H₂O)₄]·xH₂O (2 < x < 2.5) (1), [Eu(HTADIP)(H₂O)₄]·H₂O (2), [Tb(HTADIP)(H₂O)₃]·2H₂O (3), and [Er(HTADIP)(H₂O)₃]·2H₂O (4) (H₄TADIP = 5,5′-(1H-1,2,3-triazole-1,4-diyl)diisophthalic acid), have been hydrothermally synthesized and characterized. The unsymmetrical 1,2,3-triazole-containing tetracarboxylate ligand was synthesized through the copper-catalyzed azide–alkyne cycloaddition (CuAAC) reaction of diethyl-5-azidoisophthalate (M1) and diethyl-5-ethynylisophthalate (M2). Single-crystal X-ray diffraction analyses for 1–4 reveal that they are isostructural. These compounds crystallize in the monoclinic P2₁/c space group with the rutile topology. The luminescent properties of compounds 2 and 3 were investigated and characteristic Eu(III) and Tb(III) emissions are observed. Compound 3 exhibits selective luminescent sensing behavior for Cu²⁺ ions in aqueous solution. The magnetic properties of compounds 3 and 4 were studied.