The DLT algorithm is linear and fast, but it minimizes an algebraic error that has no direct physical meaning. For maximum precision, we must minimize the Geometric Reprojection Error.
The goal is to find $H$ that minimizes the distance between the measured points and the projected points:
This is a non-linear least squares problem. Since we already have a good initial guess from RANSAC/DLT, we can use iterative optimization.
The LM algorithm interpolates between the Gauss-Newton algorithm and the method of gradient descent. It is the gold standard for refining camera poses and homographies in professional vision pipelines.