Preheat oven to 375° F. Cook artichoke hearts according to package instructions, drain well and finely chop.
Sauté bell pepper in 1 tablespoon butter in a 2-3 quart heavy saucepan over medium-low heat, stirring occasionally, until softened, about 5 minutes.
Stir in artichokes and transfer mixture to a bowl.
Melt remaining 2 tablespoons butter in saucepan over medium-low heat, and then add flour, and cook, stirring, for 3 minutes.
Add half-and-half in a stream, whisking constantly, and bring to a boil. Reduce heat and simmer for 3 minutes, still whisking constantly.
Remove from heat and stir in artichoke mixture, green onions, 1/3 cup Parmesan, lemon juice, jalapenos, salt and celery salt.
Gently stir in crabmeat. Transfer to a buttered 1½-quart shallow baking dish and sprinkle with remaining Parmesan.
Bake dip in oven until bubbling, about 20-25 minutes. Serve warm with crackers or tortilla chips.