How to Make It
Bring a large pot of water to a boil. Add potatoes (make sure that they are covered by at least 1-inch of water) and cook until fork tender, about 15 minutes. Remove with a slotted spoon and transfer to a bowl to cool. Slice each potato lengthwise.
In the same pot of boiling water, cook green beans for 2 minutes and transfer to a bowl of ice water. Let stand for 5 minutes; drain and pat dry with a paper towel.
In the same pot of boiling water, boil eggs for 8 minutes and transfer to a bowl of ice water. Let cool and remove shells. Slice each egg lengthwise.
In a medium bowl, whisk together 2 tablespoons extra-virgin olive oil, lemon juice, shallot, mustard, fillets, vinegar, and tarragon until paste forms. Whisk in remaining olive oil to make dressing.
In a small bowl, mix capers and olives; toss with 1 teaspoon of dressing.
On a platter, toss lettuce with 1 tablespoon of dressing and arrange on a platter.
Divide remaining dressing evenly among potatoes, green beans, eggs, and lobster meat, and toss separately. Arrange all components over the lettuce. Top with caper and olive mixture. Season with salt and pepper, as desired.