Trim away outer layer of fennel, reserving tender stalks and any feathery tops. Quarter bulb lengthwise and cut each quarter lengthwise into very thin slices. Cut reserved stalks crosswise into very thin slices. To make fennel very crisp and slightly curled, soak in ice and cold water to cover water 1 hour, chilled.
Chop reserved fennel tops. In a bowl toss together fennel slices, fennel tops, lemon juice, oil and freshly ground black pepper to taste. Arrange salad on a platter and chill, covered up to 3 hours.
If feta is very salty, rinse under cold water and pat dry. Cut feta into 1- x 1/4-inch slices and arrange on top of salad.