If you can't remember the truth that's concerning. Anything other than the truth is technically a lie but the larger question is why can't you remember the truth? Are you suffering from memory loss, are willfully ignorant or have selective hearing when people are talking to you, or are you pathelogical liar where you believe the lies you tell yourself in your head? I'm not saying you do these things but rather these would be the questions I'd be wondering more if you were physically unable to remember the truth about something.
No. To "Lie" is to knowingly deceive.
The truth is you can't remember. Anything other than saying that is a lie.
From the description of the question you are aware that the quote is from a book and the main character of the book has anterograde amnesia.
Clearly, if you can't remember the truth; the truth is, "I don't remember". It would be a lie to say, "I don't know.," because not knowing infers you never had knowledge of the truth to begin with. This applies even in amnesia cases.