Lion-class ships would not overturn South American neutrality

Would replacing South American dreadnoughts with Lion-class battleships change when those states entered the Second World War?

No; the ships would change their capabilities after entry, but not the political reasons Brazil, Chile, and Argentina initially remained neutral.

Possession of modern capital ships is separate from the political decision to join the Second World War. Brazil, Chile, and Argentina would not enter earlier merely because their older dreadnoughts had been replaced by Lion-class ships. Their neutrality policy would still govern until outside pressure or circumstances brought them into the conflict. The new ships could affect later patrols and operations, but they would not by themselves rewrite the states' pre-entry diplomacy.