In a small bowl, combine the onion, lemon juice, and a pinch of salt and pepper and set aside.
Meanwhile, chop the endives in a cross-hatched fashion, beginning at the base and working to the point. Place the endive and watercress in a large bowl. With a slotted spoon, transfer the onion to the bowl of greens. Whisk the oil in a steady stream into the lemon juice, pour over the greens, and toss, until coated well.
Divide the salad among 4 plates and crumble the goat cheese on top.