Disordered platelet texture enables random lasing in liquid crystal blue phases, whose switchability and tunability of laser characteristics are reported in this letter. The lasing action can be switched between coherent type and incoherent type by the thermal hysteresis effect. The randomness of lasing wavelengths can be determined by the platelet size, which can be set by controlling the cooling rate. After the blue phase scattering system is polymer-stabilized, coherent random lasing may occur in both the blue phase with an extended temperature interval and the isotropic liquid state; also, the selected modes are constant from one pulse to another. Additionally, when the laser dye is sensitive to temperature, the excitation threshold and the emission spectrum may be altered by thermal control.