In a large pot, cover the potatoes with water. Bring to a boil, salt the water and cook until tender, 8 to 10 minutes; drain.
In a large bowl, whisk the lemon juice, 3 tbsp. EVOO, vinegar, mustard and sugar; season with salt and pepper. Toss with the drained potatoes, celery, shallots and tarragon; season.
Season the fish. Place the ground almonds on a plate. In a shallow bowl, whisk the eggs.
In a large nonstick skillet, heat the remaining 1 tbsp. EVOO, one turn of the pan, over medium. Melt the butter in the oil. When the foam subsides, coat the fish in the egg, then dredge in the almonds. Cook until the fish is browned and opaque in the center, about 3 minutes per side.
Divide the lettuce among plates; top with the fish. Serve with potato salad and lemon wedges.