In a large pot, bring 6 cups of water to a boil.
In the meantime, remove the bottom third of the broccolini stems and discard.
In a small bowl, whisk together, the olive oil, vinegar, mustard, garlic, and sugar. Set aside.
When the water comes to a full boil, drop in the broccolini. Return to a boil, cover, and cook over medium heat for about 2 minutes until the stalks are tender. Drain well and place in a serving dish.
Drizzle dressing over the broccolini and toss to coat. Squeeze lemon juice over the broccolini and sprinkle with a little salt and fresh pepper.
Serve warm.