Implementation of lanthanide-organic frameworks (LOFs) as solid adsorbents has been frequently handicapped by their permanent porosity being difficult to establish owing to the remarkable flexibility and diversity of lanthanide ions in terms of coordination number and geometry. Construction of robust LOFs with permanent porosity for industrially important hydrocarbon separation will greatly expand their application potential. In this work, by distributing N and O donors into an m-terphenyl skeleton, we rationally synthesized a heterofunctional linker, and constructed a pair of isostructural LOFs. Due to the inclusion of a rarely observed three-dimensional metal-carboxylate backbone serving as a highly connected inorganic secondary building unit, their permanent porosities were successfully established by diverse gas isotherms. They can be applied as separating media not only for natural gas purification and removal of carbon dioxide from C2 hydrocarbons but also more importantly for single-step ethylene (C2H4) purification from a three-component C2Hn mixture during the adsorption process. The latter separation is very challenging and has been less reported in the literature. This work provides a unique example of LOFs featuring three-dimensional inorganic connectivity applied to multipurpose hydrocarbon separations.