Earlier quoted context omitted.
Which isn't true anyway, since anonymous inner classes are just very verbose and awkward lambdas. (I'm a Java hater but I'm also a horrible pedant)
Horrible as in "no good" pedant? Because, no "anonymous inner classes" are no lambdas. They are, well, classes kludgily used to mimic a lambda proper.
Since the former have a proper name (closures) and the latter doesn't, I'd be inclined to call only the operator a 'lambda'. But since you can at least 'approximate' closures in Java (with anonymous inner classes), I think it's fair to say that they are "very verbose and awkward lambdas", to some definition of lambda.