What is the exact meaning of ‘lackadaisical’ in describing the Magliozzis who joked they were about to get “even lazier”

Solution 1:

This question is a great example of why context is so important when interpreting language. As I mentioned in one of my comments, and as JLG said in his answer, these brothers are very famously self-deprecating; it's part of their shtick. From a recent show (this is paraphrased):

Caller: I'm kind of embarrassed to say this...
Host: Go ahead and tell us – no one's listening to the show anyway.

They end each broadcast by announcing, "You've wasted another perfectly good hour listening to Car Talk" before thanking their sponsors, and then ultimately finishing with this inevitable quip:

Ray: And remember, don't drive like my brother.
Tommy: And don't drive like my brother.

As another example of how they make fun of themselves, each week's show includes a "Puzzler" – a brain-teaser of shorts. In the written version of the puzzler (found on the show's website), the puzzler reads:

You begin to paddle upstream. You get a mile from where you put your boat in the water, and your hat flies off. You say, "Ah, forget it!" You keep rowing.

Yet, when they presented the puzzler during their show (here's the podcast), they say:

...your hat flies off. It's just a Car Talk hat, so you say, "Ah, forget it!" You keep rowing.

Understanding how these two hosts continuously make fun of themselves during their broadcasts is key to appreciating the gibe in their announcement: retirement is a chance for them to get "even lazier" (as if they'd never been working hard anyway). The reporter, merely "going along" with the act, proceeds to call them "famously lackadaisical," creating a one-liner that's almost sure to bring a knowing smile to the face of any regular listener.

Solution 2:

I love "Car Talk" and Tom and Ray Magliozzi! They are famous for their self-deprecating humor on their long-running radio call-in show as they help car owners with their vehicular (and relationship) troubles. They are both very smart, MIT-educated men, but they are also very down-to-earth, get-under-the-hood, get-their-hands-dirty mechanics. They laugh a lot and don't take themselves too seriously. I think they probably do put some effort into their show (they show up week after week, after all), but they also are able to enjoy themselves. In this instance, I think this is a better definition of how the writer is using lackadaisical: nonchalant, relaxed in manner.