Lestat lies about the reason the “witches”burned. He lies about the depth of his relationship with Nicki & simultaneously ensures the truth of it isn’t recorded. He lies to protect their memory & their dignity.
His anger with the book stems from Louis sharing Lestat’s trauma and assault without his consent. He is hurt by the exploitation of his abuse and by Louis’ betrayal of his trust and vulnerability. He resolutely will not subject Nicki (who he deeply loved) and the girls (who he cared for and/or relates with in regards to their similar histories of victimization) to the same treatment of becoming publicly consumed for entertainment’s sake.
This is the so-called “unreliability” of Lestat’s narration. He will lie and distort truths - not because he doesn’t remember correctly or for the sake of inflating his ego. It’s done intentionally - as a means of protecting others or as an attempt at self-protection from the realities of the repeated abuses he was subjected to throughout his life.
It’s unsettling that people are often unwilling to see (or accept) how considerate, thoughtful, and empathetic Lestat can be, or when his anger with Louis about the book is trivialized to minor disagreements and petty slights.