I think it was a combination of a couple of things -- the fact that she's a very talented bender probably contributed, and I could see lightening bending having a calming effect on her too. But, while I've definitely not had a mental breakdown as severe or complete as Azula's was, I've had some pretty serious panic attacks and it's weird but I always feel more centered/in control after them than I did before. I could be way off base with Azula, but I'm thinking she might have had a similar experience.

as what anaswill said, i too believe that it's a combination of a few things. azula is very talented bender, being viewed as a prodigy and being the only one known to be able to conjure blue fire. she could have already had an expertise in generating lightning seeing as how she did it while she was breaking down. sozin's comet possibly helped her to conjure lightning even without the proper mindset. though, perhaps it could also be that her goal to kill zuko allowed for some clarity.
azula also attacked zuko with lightning in the search (despite being put in a straitjacket), so this definitely proves how skilled she is in lightning generation. she conjured it a few times despite being a victim to her insanity during the search.

I've also thought that it was a combination of things. At first I thought it may have just been the comics, but as you pointed out, she was still able to do so in The Search. Which is why I think it's both that she's powerful enough a bender as well as lightning bending in itself is comforting to her. In the picture I used for that option I feel as though she looks much calmer than she did throughout the rest of the Agni Kai.