Coarsely chop shrimp. Melt butter in a skillet over medium heat. Add shrimp, garlic, and green onions and cook just until the shrimp are pink, 2-3 minutes. Stir in lemon juice.
Reduce heat to low and add cream cheese, stirring until melted. Add sour cream, mayo, Parmesan, and mozzarella cheese, and stir until combined.
Season with salt and pepper, then spoon mixture into a 1-quart baking dish and sprinkle top with paprika.
Bake for 30 minutes, or until lightly browned and bubbly. Serve with pita chips or crackers.
Notes
To mix this dip up ahead of time, follow the stove top steps in the recipe, then cover and refrigerate. When ready to cook, preheat oven, remove from the refrigerator and bake uncovered as directed.