What is the force required to lift the balloon with
V=1500m3 and m=420kg, containing air with density 0.8kg/m3 and moving in air with density 1.3 kg/m3?

No force is required to lift that balloon. In fact, force is required to hold it down, and if you let go, it's up, up, and away.

Since the balloon's density is less than the density of the air around it, it's lighter than the air it displaces, there is a net upward buoyant force acting on it, and it floats up !