Season grouper with salt, pepper, and paprika. In a medium-sized skillet, heat butter and olive oil over medium heat. Sear fillet on both sides, cooking until fish is done throughout; be careful not overcook. Remove from heat and set aside.
Slice avocado and squeeze lemon juice over avocado to prevent browning. To assemble club, spread mayonnaise on first slice of toast, face up. Place 1 slice tomato, sprouts, and grouper on top. Spread mayonnaise on second slice of bread and put on top of grouper, mayonnaise side down. Spread mayonnaise on top of second slice. Top that with avocado slices, 1 tomato slice, more sprouts, and the bacon. Spread mayonnaise onto third slice of bread and top the sandwich. Cut into fourths and place a toothpick in each piece.