I think שום דבר almost always goes with לא. I can think of two exceptions, quite common actually.
(1) When this is the complete answer to a question, such as "What are you doing?" or "What is in the bag?" English answer: "Nothing." Hebrew: שום דבר.
(2) When saying in English "It's nothing" about something, to make it seem a trifle - for example, about some wound or pain, or when someone thanks you for taking some trouble to help them. In Hebrew: "זה שום דבר".