Heat butter in large skillet. Add carrots and sauté over medium heat, stirring frequently until crisp-tender and beginning to turn golden (8-10 minutes). Add broccoli and continue cooking for another 4-5 minutes. If the skillet begins to dry up, add some of the apple juice while sautéing. When the vegetables are crisp-tender, add the remaining apple juice and sauté, stirring, until it is absorbed. Stir in lemon juice, chives and pecans. Cook for an additional minute, then transfer to a serving dish and serve immediately.