To transform bound state-in-continuum (BIC)-related unidirectional radiation into BIC-related unidirectional lasing, a 1-D grating with a parity-time (PT)-symmetry configuration is proposed. Through non-Hermitian modulation, the BIC undergoes an asymmetric split in the –k and +k spaces. Abnormal phenomena have also been observed. The asymmetric BIC makes the grating either a gain cavity or a loss cavity depending on the incident direction of the plane wave. With plane wave incidence, the grating exhibits Fano resonance with energy conservation. However, for diverging light incident from a line source or a Gaussian source, the coupling of the gain cavity and loss cavity produces a new phenomenon, unidirectional and single-mode lasing with an interesting wavefront transformation from a diverging wave to a unidirectional plane wave. The physical mechanism is explained by the joint effect of the asymmetric PT-BICs and cavity resonance.