Why did Alex lie about the ticket?
I don't understand what Alex hoped to gain by lying and saying that he bought Juliet's and ticket, and that they were going together. At this point he knew that Juliet betrayed him and David, and was going to take the money for herself and run.
Was it just to mess with David? He should have been interested in David (and Juliet) getting out of the flat as soon as possible, before they realized they were had.