AM is one slippery character but he’s not dumb. I can imagine that he knew he’d be Suspect Number One…from those first hours. He does hand everything over quote willingly…his phone,etc.
We also know that AM is a stellar liar…for most of his life, an incredibly successful one. He has lied and hidden all sorts of criminality…from family, friends, law partners, clients.
I am no longer sure that AM‘s Big Lie is evidence of guilt. It could just be that he knows he will be a suspect, so hes protecting himself by using his most reliable skill-set…lying.