The broadcaster's private life became public knowledge when pictures emerged of her ex-husband Charles Saatchi holding her by the throat and she had to give evidence at the trial of two of her staff.
Appearing on the comic's BBC chat show, Lawson said: "Well, you know, I've had better times. You know, it's spring and I'm feeling better and I'm very happy to be here."
The star said her recent struggles had made her more sympathetic to other people's problems, saying: "We all gossip but I don't take a particular lofty view. Perhaps having a layer of skin removed I'm also more aware of other people's misfortunes.
"If I read something in magazine I can't remember [it], so why would they remember about me? I really think that if the major thing in your life is what people who don't know you think, then you're living your life wrong."
The other guests on the show, which is on BBC1 on Monday at 10.35pm, are survivalist Bear Grylls and musician Gary Barlow.