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/coinductive characterisation of the logical relation recently discovered by the author.