Yes, in Aruba, I would recommend Don Carlos Restaurant right in the heart of Oranjestad if you want lobster. They have a tank and you pick the lobster (s) you want and they cook it for you on the spot.
Also, I would highly recommend the Havana Beach Club just a short walk from the cruise terminal. Go out to the main street, turn right, past the marina until you see its sign. It is a local restaurant/bar/beach club that is frequented by locals. Very few cruise passengers make it here. It is awesome.