The oil lamp is an old image of wisdom and watchfulness, light that must be tended to keep burning. Running out of oil is read as exhaustion or neglected preparation.
Does the traditional reading fit your dream, or did it mean something else to you?
My Cosmic Code has a private dream journal. Write a dream down and the app picks out the symbols in it, shows what dream books say about them and, over time, which words recur across your entries. The journal is stored on your device only.