Bring a pot of lightly salted water to a boil; add artichoke heart. Cover pot and cook artichoke until tender and leaves pull off easily with a fork, about 45 minutes. Run artichoke under cold water and remove and refrigerate all the leaves. Scoop and discard the hairy part of artichoke heart.
Heat olive oil in small saucepan over medium heat; cook and stir onion and garlic until onion is translucent, 5 to 10 minutes.
Blend artichoke heart, onion mixture, vegan mayonnaise, mozzarella-style vegan cheese, salt, and lemon pepper in a blender until almost smooth. Transfer dip to a bowl and refrigerate for flavors to blend, about 1 hour. Serve dip with artichoke leaves.