In a small bowl, whisk together the lemon juice, shallot, and mustard and then gradually whisk in the olive oil to create an emulsion. Add the tarragon; season to taste with salt and pepper. Refrigerate until serving time.

Bring a medium pot of salted water to a boil over high heat. Add the lemon juice and the prepared artichoke bottoms. To keep the artichokes from bobbing to the top, weight them with a pot lid that's smaller than the boiling pot. Keep the pot uncovered and adjust the heat to maintain a gentle simmer. Cook until the artichokes are tender when pierced with a knife, about 20 minutes. Drain upside down on paper towels until cool.

Tear the lettuce into bite-size pieces. Halve each artichoke bottom and cut each half into 5 or 6 wedges. Put the artichoke wedges in a salad bowl and add 2 tablespoons of the vinaigrette; toss to coat. Add the lettuce and the remaining dressing and toss gently. Arrange the salad on six plates and garnish with the egg wedges. Serve immediately.