The aqueous medium reactions of lead(II) nitrate with H2ATIBDC as a main ligand and bipy or biim as an auxiliary ligand lead to the two fascinating coordination polymers: [Pb(ATIBDC)(bipy)(H2O)]·3H2O (1) and [Pb(ATIBDC)(biim)]·H2O (2) [bipy = 2,2′-bipyridine, biim = 2,2′-biimidazole, and H2ATIBDC = 5-amino-2,4,6-triiodoisophthalic acid]. The interesting chiral three-dimensional (3D) network [Pb(ATIBDC)] (3) is obtained in the absence of any auxiliary ligands. Complex 1 is a one-dimensional (1D) helical chain, which further arrays into a 3D supramolecular metal–organic framework (MOF) with a 1D channel through the hydrogen-bonding and strong offset π⋯π stacking interactions. Furthermore, a 1D hydrogen-bonded helical water chain was found in 1. Interestingly, complex 1 exhibits reversible adsorption/desorption to water molecules. Framework 1 falls within the category of “recoverable collapsing” and “guest-induced re-formation” frameworks. Complex 2 features a fascinating 3D MOF. It displays a novel four-connected 4668-SOD (sodalite) zeotype network structure with 1D nanotubular channels. Complex 3 crystallizes in the chiral space group P31 and possesses a 3D honeycomb-like structure built up from a 1D Pb(II)-carboxylate-bridged helical chain with a 31 helix and ATIBDC2− ligand. The coordination modes of the ATIBDC2− ligand and crystalline architectures of the complexes are greatly dependent on the auxiliary ligands. The thermal stability and solid state fluorescent properties have been studied. Adsorption/desorption properties reveal that 2 may be used as an adsorbent material for some guest molecules. The study broadens the still very limited use of H2ATIBDC as a spacer and lead(II) ion for crystal engineering of MOFs with channels and cavities. These compounds represent the first examples of lead(II) complexes with H2ATIBDC.