Comment by t_mann

The thing is, Lagrangian mechanics makes exactly the same predictions as Newtownian, and it starts from a foundation of just one principle (least action) instead of three laws, so it's arguably a sparser theory. It just makes calculations easier, especially for more complex systems, that's its raison d'être. So in a world where we don't know about relativity yet, both make the best predictions we know (and they always agree), but Newton's laws were discovered earlier. Do they suddenly stop being natural laws once Lagrangian mechanics is discovered? Standard physics curricula would not agree with you btw, they practically always teach Newtownian mechanics first and Lagrangian later, also because the latter is mathematically more involved.