Understandably, you can conjecture that the LaGrangian function is the foundation of LaGrangian dynamics. From the Principle of Hamilton, you can derive LaGrang's Equation. You also can show that LaGrange's Equation and Newton's Second Law are the same. There are several reasons. The first is that you can use energy to model the physical situation.
Energy is a scalar function.
You need not first think about vectors in LaGrangian dynamics. The second reason is that you can use generalized coordinates. Therefore you can more simply and more naturally describe the situation using more sensible coordinates. Finally you must solve the Lagrange's Equation. Another advantage of LaGrange's dynamic is the method of LaGrangian multipliers.