If the lights stop working because a storm interrupts the electricity then you say they WENT out. If a person flips the switch then the lights are "turned off". Candles GO out. A person cannot "turn off" a candle though he can "put it out" or "blow it out".

The lights are going to be switched off tonight. The fire went out. (Died out) The lights went off or out. (They tripped) Hope that gives you more of a clue.

By the way, “go off” is more often seen in set phrases. We use “go off” with a person “going off against (or on) someone else” often angrily. “The visiting vice president from HQ really went off against the account manager in the meeting yesterday because his account had so many past due invoices.” Or “go off on a tangent” which is to talk about an unrelated subject. “The same account manager would often go off on tangents in business meetings talking about the favorite sports teams of his clients at length.”