Bring broth, salt, and 1 tablespoon sugar to boil in a 12-inch nonstick skillet. Add carrots, reduce heat to medium, and simmer, covered, for about 5 minutes, until the carrots are almost tender when poked with the tip of a paring knife. Uncover, increase heat to high, and cook, stirring frequently, until the liquid has reduced to about 2 tablespoons, about 1 to 2 minutes.

Add butter and remaining 2 tablespoons sugar to the skillet. Toss to coat and cook, stirring frequently, until the carrots are tender and the glaze is light gold, about 3 minutes. Off heat, add lemon juice and toss to coat. Season to taste with freshly ground pepper. Serve immediately.