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Preheat oven to 350 degrees F. Coat a 9″ x 13″ baking dish with non-stick cooking spray; set aside.
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Rinse filets, and pat dry with paper towels. Lay the tilapia filets in a single layer in the prepared baking dish.
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Squeeze lemon juice over fish, being careful not to let any seeds get into your pan.
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In a medium bowl, combine Parmesan, butter, mayonnaise, chives, Old Bay, salt, pepper, and basil until smooth.
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Bake fish for 15 minutes, until opaque and just starting to flake. Carefully remove baking dish from oven. Spread 1/4 butter mixture over each of the tilapia filets.
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Bake for another 5 minutes, until butter mixture melts and coats fish.