I don't believe that there is such a thing as "offensively lazy". The sets "lazy jokes" and "lazy jokes that have the power to cause offense" are not equivalent.

Have you ever seen somebody appear offended by "Why did the chicken cross the road?" "So how about that airline food?" "'Knock knock.', 'Who's there?', 'Banana.'" "Can I has cheeseburger?"

Those are all lazy jokes. As lazy is as is possible. Yet their laziness lacks the power to offend. No sane person is going to become offended by somebody dredging up some lame 10 year old joke about cats that like to eat cheeseburgers. Wherever you find an example of a "joke that is so lazy, it is offensively lazy", there is without fail a more plausible explanation for the offense the joke elicits.

For example, "Australians are upside-down". Lazy, and makes many people upset. Are they upset because it is lazy? No, they are upset because it is picking on other people (themselves or others).