So why is it “Lord God” now (at, e.g., Gen 2:4) and not just “God”?

It is a two-word phrase, יְהוָ֥ה אֱלֹהִ֖ים or yahweh elohim. Some critical purveyors of the Documentary Hypothesis make much of this, thinking it is the “Yahwist” who wrote these texts. This is more easily explained by saying that God, since he will presently have a man to rule over, can be called the sovereign lord—is a good gloss of the etymological and connotative meaning of the name “Yahweh”—in addition to “God.”