"We lived a lie," said Maxim. What did he mean

This is Maxim's confession about the murder. Maxim no longer appears to have any desire to keep the murder a secret. When Maxim refuses to give blackmail money to Jack Favell and calls Colonel Julyan, he is in essence making the decision to let the truth come out. Nevertheless, by making himself a willing sacrifice, Maxim ultimately undercuts Rebecca’s power over him. Since her death, Rebecca has maintained control over him, determining his choices and actions, even in his marriage with the narrator. By calling Colonel Julyan himself, Maxim takes control of his life and ensures that he will no longer be crippled by the fear that someone will find out the truth about Rebecca.