There are provided a discharge lamp drive apparatus which can detect that both ends of at least one of a plurality of discharge lamps is in an open state in a differential drive scheme, and a liquid crystal display apparatus. A first current detection circuit 31 detects a current flowing through a first discharge lamp connection terminal group P1 or a current flowing through a second discharge lamp connection terminal group P3, and generates a first current detection signal S1. A second current detection circuit 32 detects a current flowing through the second discharge lamp connection terminal group P2 or a current flowing through a fourth discharge lamp connection terminal group P4, and generates a second current detection signal S2. A signal processor 30 receives the first current detection signal S1 and the second current detection signal S2, and generates a signal S01 which is used to detect an open state of a discharge lamp based on intensities of both the current detection signals S1 and S2.