[lmkg]

The function returned by 'compose' is a closure because it captures references to its local environment (the two functions passed to 'compose'). If it did not close over these variables, it would not work. It might be possible to define a limited 'compose' operator in a language without closures that worked at compile-time/define-time, but you wouldn't be able to choose functions to compose at run-time like you could with a capturing 'compose.'

Nitpick: Lambdas and closures are different things. A closure is a semantic notion of a function captures its local environment. A lambda is a mostly-syntactic notion of defining a function without giving a name. Whether a lambda is a closure depends on the language's scoping rules.