Two recently observed ²⁹³Lv (Z = 116) α-decay chains [Eur. Phys. J. A 48, 62 (2012)] are investigated in the framework of covariant density functional theory with PC-PK1, where the pairing correlations are treated by the Bardeen–Cooper–Schrieffer method with a density-independent zerorange force. From the calculated potential energy curves, it is found that two minima always occur, with one having an almost spherical shape and the other exhibiting a large deformed prolate shape. Originating from the ground state and the shape-isomeric state of ²⁹³Lv, the two observed α-decay chains are constructed and the calculated Q_αvalues are found to be in good agreement with the data.