@BlueFootedBooby allow me to start out by stating that I agree with reducing meat consumption. What we do now as a country is unsustainable.
As for the link provided: it undercuts your point. "we demonstrate that under a range of land use conditions, diets with low to modest amounts of meat outperform a vegan diet, and vegetarian diets including dairy products performed best overall." This study, you provided, shows lacto and ovovegatarian diets performed almost identically under most cases