This note gives a new proof of the `operational extensionality' property of Abramsky's lazy lambda calculus--namely the coincidence of contextual equivalence with a co-inductively defined notion of `applicative bisimilarity'. This purely syntactic result is here proved using a logical relation (due to Plotkin) between the syntax and its denotational semantics. The proof exploits a mixed inductive/co-inductive characterisation of the logical relation recently discovered by the author. (Full version of an invited paper presented at the 3rd Workshop on Logic, Language, Information and Computation (WoLLIC'96), May 8--10, Salvador (Bahia), Brazil, organised by UFPE and UFBA, sponsored by IGPL, FoLLI, and ASL.)