Heat grill to medium-high.
Season the steak with ¾ teaspoon salt and ½ teaspoon pepper. Grill to the desired doneness, 4 to 5 minutes per side for medium-rare.
Meanwhile, in a bowl, gently toss the fennel, oil, ½ teaspoon salt, and ¼ teaspoon pepper.
Grill the fennel, turning occasionally, until just tender, 5 to 6 minutes. Transfer back to the bowl.
Grill the lemon slices until slightly charred, 1 to 2 minutes per side. Toss the lemons with the fennel and thyme. Serve with the steak and mozzarella.