Preheat oven to 375°F (190°C).
In a medium bowl, combine the softened cream cheese, sour cream, and mayonnaise until smooth and creamy. An electric mixer can be used for a smoother consistency.
Gently fold in the lump crab meat, taking care to keep some of the lumps intact.
Add the Monterey Jack cheese, cheddar cheese, Parmesan cheese, fresh dill, lemon juice, Old Bay seasoning, smoked paprika, garlic powder, and cayenne pepper (if using). Stir until just combined. Be careful not to overmix. NOTE: You can serve it as a delicious Cold Crab Dip at this point, or continue for Hot Crab Dip.
Transfer the crab mixture to a shallow oven-safe dish or pie plate. Top with extra cheddar cheese, if desired.
Bake for 25-30 minutes, or until the dip is hot, bubbly around the edges, and lightly golden on top.
Let the dip rest for a few minutes before serving warm with your choice of crackers, baguette slices, or fresh vegetables.