Melt butter in a large skillet over medium heat; add garlic, fennel, and celery. Sauté 5 minutes. Add fish and red pepper, turn off heat, and leave pan on burner 3 minutes. (Fish will cook with residual heat.) Let cool.
Whisk together half-and-half and egg in a medium bowl; add flour and whisk until smooth. Gently fold in lionfish mixture, cilantro, green onions, and salt.
Heat oil to 350° in a 2-quart pot over medium-high heat. Drop batter, about 2 tablespoons at a time, into hot oil, using a large metal spoon to keep fritters separate. (Allow fritters to take on a natural shape.) Working in batches to keep oil at a constant heat, cook fritters, gently turning with a spoon to ensure even cooking, 3 minutes or until dark golden brown. Remove fritters to a paper towel-lined plate; serve with Red Bell Pepper Coulis.