Does low pressure induces high velocity or high velocity induces low pressure?
Neither! The cause is wing moving through the air, and the effect is a fairly complex flow pattern around it that produces lift (and wake vortex).
We know that the flow obeys certain laws (that are largely averaging of the microscopic laws governing individual molecules). One of them is law of conservation of energy, which for fluids is known as Bernoulli's equation. But that's just one equation with many free variables, so alone it is not enough to explain anything. You need the complete set of Navier-Stokes equations to be able to describe the flow.
The equations are partially differential, and need to be evaluated for every point in space and time, which can only be done approximately and requires a computer.
There is only a few conclusions that can be made using conservation laws without this, the most important probably is the existence of downwash. The third law of motion tells us that if upward force, lift, is applied to the wing, downward force is applied to the air, and second law of motion tells us that this force accelerates the air downward. The boundary between downward moving air behind the wing and the still air outside the span is the wake vortex.
But again, neither is cause and effect. The laws of physics work both ways. They just tell us that these phenomena always occur together. But the cause is the situation. We just know that both or neither will occur.