Droplet manipulation under various physical fields is crucial for microfluidics. Theoretical models are key to understand the physics. In this work, by extending the binary phase lattice Boltzmann model to fully coupled thermodynamics and electrostatics, we systematically explore the behaviors of droplet transport driven by temperature-dependent surface tension, thermocapillary, and electrowetting effects. It is shown that electrowetting enables bidirectional transport of the droplet, determined by various physical parameters such as electric voltage, wettability, viscosity, thermal conductivity, and surface tension. Specifically, the physics revealed in this work is more than simply electrowetting modified wettability. Actually, the droplet transport is controlled further by contact angle hysteresis and thermocapillary-induced temperature gradient.