One way to do dynamic path finding is have the entity predict where the target is going and go there.
One way of doing this is using a Taylor series.
I'll call the path of the target over time the function S(t) where S is the position and t is the current time and the approximation to the path is A(f) and f is the date in the future one is approximating.
Then the simplest and most stupid approximation is A(f)=0.
The next simplest is A(f)=S(t) where t is the current time and f is the future.
This is predicting the target simply stops in place.
The third simplest is A(f)=S'(t)*f+S(t) where S' is the derivative of S with respect to time.
This is predicting the target continues on at a constant speed with no acceleration.
The fourth simplest is A(f)=S''(t)*f^2/2+S'(t)*f+S(t).
This is predicting the target is accelerating at a constant speed like a falling ball.
I know this can be rephrased in terms of change in time which is probably more convenient for a game.
Now S can be anything. It could be an X coordinate, it could be a Y coordinate, it could be the distance between the objects, it could be an angle.
Also there's probable better methods of predicting the future path of an object so I'd look around a bit.