Look for fennel bulbs with delicate green fronds still attached to the ends of the stalks. Most bulbs also have small wisps inside, near the core.
Trim outer layer of fennel bulbs; cut stalks from tops. Roughly chop enough green fronds for about 2 tablespoons; set aside. Using a mandoline or sharp knife, slice bulbs crosswise as thinly as possible. Discard tough core. Place sliced fennel bulbs and reserved chopped fronds in a salad bowl; add almonds.
Make dressing: In a small bowl, whisk together lemon juice, oil, and salt, and season with pepper. Pour dressing over fennel mixture; toss well to combine. Serve immediately.