Bring 4 quarts water to a boil in a large saucepan; add 1 teaspoon salt. Cook Broccolini in batches for 5 minutes; remove with a slotted spoon. Drain. Discard water.
Combine butter, rind, and juice, stirring with a fork until well blended. Return Broccolini to pan over medium-high heat; stir in butter mixture, remaining 1/8 teaspoon salt, and pepper, tossing gently to coat.