Prepare an ice-water bath. Bring a large pot of generously salted water to a boil. Cook broccolini until tender, about 4 minutes. Drain, and transfer broccolini to ice-water bath. Drain again and pat dry with paper towels.
Heat oil in a large high-sided skillet over medium-high heat. Cook lemon zest until sizzling, about 30 seconds. Add broccolini and cook until warmed through. Transfer to a platter and season with salt and lemon juice.
Blanched broccolini can be refrigerated for up to 2 days. Saute with lemon zest just before serving.