Herbed butter can be made ahead of time and used on other vegetables, fish, or chicken.
Place butter in the bowl of an electric mixer fitted with the paddle attachment, or in a heavy bowl, with lemon zest and juice, dill, garlic, salt, and pepper. Beat until well combined. Transfer herbed butter to a piece of parchment or wax paper, and roll into a cylinder, twisting both ends to secure. Place in refrigerator until ready to use.
Place a saucepan with steamer insert and 1 1/2 inches water over medium-high heat. Trim sprouts of outer leaves, and cut a small X in each base with a paring knife. When water in steamer is boiling, add sprouts and lemon quarters. Cook until sprouts are tender and bright green, tossing occasionally, about 10 minutes.
When sprouts are done, discard lemon, and transfer to serving bowl. Cut disks of herbed butter, and toss with sprouts. Serve sprinkled with fresh dill.