Whisk 3 tablespoons olive oil and next 5 ingredients in small bowl. Season dressing to taste with salt and pepper.
Heat remaining 1 tablespoon oil in nonstick medium skillet over medium-high heat. Add prosciutto and sauté until crisp, about 4 minutes. Transfer prosciutto to paper towels to drain.
Fill medium bowl with cold water. Squeeze juice from lemon halves into water; add lemon halves. Cut off stem from 1 artichoke, then bend back all outer leaves and snap off where leaves break naturally (only small cone of pale green inner leaves will remain). Trim off all dark green parts. Cut out and discard choke. Slice artichoke bottom very thinly. Place in lemon water. Repeat with remaining 3 artichokes. Do ahead Dressing, prosciutto, and artichokes can be made 2 hours ahead. Let stand at room temperature.
Drain artichokes well; transfer to large bowl. Add 2 tablespoons lemon juice and sliced fennel; toss. Mix in frisée and dressing; toss. Season salad with salt and pepper. Sprinkle with prosciutto and chopped fennel fronds.