In S05E04, after Luther and Alice have just dropped off Mark and are still parked outside, they have this conversation:
ALICE: What about the George Cornelius problem? Have you dealt with it?
ALICE: Let's not be coy. Is he dead, John?
ALICE: Because it's the only way. He'll kill us both. You do know that?
LUTHER: Alice, it's done.
ALICE: You wouldn't lie to me, would you, John? Not about something this important.
ALICE: Because you're the only person I ever knew who always told me the truth.[SIGHS] Come what may. You never lie to me.
LUTHER: It's done.
Immediately after, Alice gets out and Luther drives off. Alice then calls George Cornelius to find that he is still alive.
Why did Luther make such an obvious lie to Alice?