In-plane integration of various two-dimensional materials has recently emerged as an exciting approach to the tailoring of desired properties for novel nanoelectronic devices. Type-II lateral heterostructure (LHS) semiconductors with direct bandgap are urgently desired in photovoltaic, photocatalytic and optoelectronic devices. In this work, we design novel AsmPn LHSs with excellent stability composed of blue phosphorene and arsenene along the zigzag interline. In contrast to the wide indirect band gaps of pristine blue phosphorene and arsenene, all LHSs considered here except As2P2 possess narrower, direct gaps. As2P2 is an indirect-gap semiconductor with quasi-type-II band alignment, while the other LHSs are direct-gap semiconductors and have type-II alignment with the electrons (holes) located in monolayer blue phosphorene (arsenene). In addition, it is found these LHSs have high carrier mobilities of up to cm2 V−1 s−1. Interestingly, several attractive characteristics of BP/arsenene LHSs, including direct bandgap and high mobility, can be well preserved even if the component ratios and tensile strains are changed. As4P4 undergoes a transition from type-II to type-I-like band alignment at when we apply tensile strain along the x direction, while a transition from type-II to type-I alignment is observed at if the tensile strain is applied along the y direction. Furthermore, we have found that the energy gaps of LHSs can be effectively manipulated via the strain, width and component ratio. Our predictions highlight the potential applications of blue phosphorene/arsenene LHSs in electronics, photovoltaics, optoelectronics and photocatalysis.