I actually
caught him lying on a couple of occasions, at least to my own reading of the book.

Could you list the times when he's definitely lying - I mean, those where it can be proven?
Now, I don't have the book on me at the moment, so I can't provide exact page references or quotes--however, I believe there is substantial evidence that what he said about the Cardassian mindset, about Cardassians not dwelling in the past/living in a sort of eternal present and only worrying about the future is flat-out wrong. I have evidence both within the book and outside it (i.e. canon) that makes it very clear this is not true. The statement was almost certainly put there by Garak in an attempt to keep Bashir from pitying him, and yet the text belies it. We see him use it in a particularly harsh manner once to stop Bashir's line of inquiry as he recalls his time on DS9 with Bashir, which sheds some very obvious light, in my opinion, on the purpose of Garak's obfuscation.
We have one Obsidian Order agent (Maladek) who is clearly described as cracking
because he was betrayed back at Bamarren--NOT because of anxiety about the future. Had he been able to let go of is past betrayal by the Charaban team, to compartmentalize that as Garak claims, this would not have been an issue.
We then have Skrain Dukat in two instances, both canon and within the book, very clearly demonstrating how obsessive he can become over past events: Dukat becomes obsessed with revenge against Garak after the death of his father. Really, Dukat? HOW good are you at not being anxious about your past, but ONLY your future? But the ultimate instance with Dukat is the way he cracks in "Sacrifice of Angels." Indeed, his delusion that Ziyal is alive--and his subsequent delusions that he is being ridiculed by those he knew in his past (in "Waltz")--is the ultimate example of living in the past. Add to that how hung up on the Occupation he is, how he defines himself by believing that the Bajorans LOVED him (past tense!), and when Sisko breaks him once and for all on this, in "Waltz", his mind cannot withstand it and it sends him into a final tailspin. And all this because his illusion of the past was destroyed!
The final evidence, though, is two things in Garak's life. Why can he not forget Palandine? Why is he unable to stop wondering what happened to her, instead of simply moving on? Why does this past event continue to affect him? And finally, we have Garak's action in writing to Bashir. Yes, he is indeed uncertain about the future of the Cardassian Union, but why is turning to his past--to Bashir--is highly questionable. And it looks an awful lot like a man trying to absolve himself of his regrets before he CAN move on into that future.