Preheat the oven to 400 degrees F. Spread the walnuts on a baking sheet and toast in the oven until golden, about 5 minutes. Let cool slightly. Meanwhile, bring a large pot of salted water to a boil.
Puree the olive oil, parsley, garlic, lemon zest, lemon juice and 1/4 teaspoon salt in a food processor or blender until smooth. Add the gruyere, olives and toasted walnuts; pulse until coarsely chopped, about 1 minute. Transfer the pesto to a large bowl.
Add the potatoes to the boiling water and cook until tender, about 8 minutes. Remove with a slotted spoon and transfer to the bowl with the pesto.
Add the pasta to the boiling water and cook until al dente, 10 to 12 minutes, adding the lettuce during the last 1 minute. Reserve 1/2 cup cooking water, then drain the pasta and lettuce and transfer to the bowl with the pesto. Toss to coat, adding enough of the reserved pasta cooking water to loosen the sauce.