The phase behavior of ABCD tetrablock copolymer melts is studied using self-consistent mean-field theory. In particular, the noncentrosymmetric (NCS) lamellar phase (with sequence...ABCDABCD...) and the centrosymmetric (CS) lamellar phase (...ABCDDCBA...) are examined in two cases. First, an enthalpically stabilized NCS lamellar phase is investigated by varying the interaction between the A and D blocks from repulsive to attractive while keeping all block lengths equal. In the second case, an entropically stabilized NCS lamellar phase is investigated by changing the lengths of the two end blocks, which are taken to be chemically identical (ABCA tetrablock melt). In both cases, the NCS phase is found in regions of the phase diagram, and direct disorder to NCS transitions are possible. In addition, two partially mixed centrosymmetric (MCS) lamellar phases are observed between the disordered and fully ordered (NCS and CS) phases. This study extends our previous work on triblock-diblock blends which revealed an entropically stabilized noncentrosymmetric lamellar phase.