As many of you may know, there is a classical example of the Operation enum (using Java 8 standard interface now though), that is the following:
I'm surprised no one mentioned this, but the lambda approach can get hairy when implementing multiple methods. Passing a bunch of nameless lambdas into a constructor will be more concise, but not necessarily more readable.
Also, the benefit of using a lambda decreases as the function grows in size. If your lambda is more than several lines long, an override might be just as easy to read, if not easier.