1. Place a large bowl of ice water in the sink. Bring a large pot of salted water to a boil over high heat. Add green beans and return to a boil. Cook until beans are tender, 3 to 5 minutes. Using a slotted spoon, quickly transfer green beans to ice water to stop cooking. Drain and lay out on paper towels to dry. (Can be done up to 3 days in advance to this point. Wrap in damp paper towels, cover with plastic wrap and refrigerate. Bring to room temperature before serving.)
2. In a large bowl, whisk together vinegar, lemon juice, 1/4 tsp. salt, 1/8 tsp. pepper, mustard and shallot until blended. Slowly add both oils, whisking constantly, until thickened. (Can be made up to 3 days in advance, minus the shallot. Keep chilled in a glass jar with a tight-fitting lid. Add shallot right before using.)
3. Just prior to serving, add beans to bowl with vinaigrette. Toss well and season with additional salt and pepper, if desired. Serve at room temperature.