The emergence of early life must have been marked by the appearance in the prebiotic era of complex molecular structures and systems, motivating the investigation of conditions that could not only facilitate appropriate chemical synthesis, but also provide the mechanisms of molecular selection and structural templating necessary to pilot the complexification toward specific molecular patterns. We recently proposed and demonstrated that these functions could be afforded by the spontaneous ordering of ultrashort nucleic acids oligomers into Liquid Crystal (LC) phases. In such supramolecular assemblies, duplex-forming oligomers are held in average end-to-end contact to form chemically discontinuous but physically continuous double helices. Using blunt ended duplexes, we found that LC formation could both provide molecular selection mechanisms and boost inter-oligomer ligation. This paper provides an essential extension to this notion by investigating the catalytic effects of LC ordering in duplexes with mutually interacting overhangs. Specifically, we studied the influence of LC ordering of 5'-hydroxy-3'-phosphate partially self-complementary DNA 14mers with 3'-CG sticky-ends, on the efficiency of non-enzymatic ligation reaction induced by water-soluble carbodiimide EDC as condensing agent. We investigated the ligation products in mixtures of DNA with poly-ethylene glycol (PEG) at three PEG concentrations at which the system phase separates creating DNA-rich droplets that organize into isotropic, nematic LC and columnar LC phases. We observe remarkable LC-enhanced chain lengthening, and we demonstrate that such lengthening effectively promotes and stabilizes LC domains, providing the kernel of a positive feedback cycle by which LC ordering promotes elongation, in turn stabilizing the LC ordering.