Avocado and Grapefruit Salad

2 tablespoons verjus* or 3 1/2 teaspoons white grape juice and 2 1/2 teaspoons apple cider vinegar
2 tablespoons fresh lemon juice
2 tablespoons minced shallot
1/4 cup walnut oil
1/4 cup olive oil
Fine sea salt
8 large butter lettuce leaves
3 ripe avocados, halved, pitted, peeled, thinly sliced, rinsed under cold water
3 large Ruby Red grapefruits, all peel and white pith cut away, segments cut from between membranes 

* Milder than vinegar, verjus is a tart juice made from unripe grapes; available at specialty foods stores and from chefshop.com and terrasonoma.com.