1. Preheat grill to 350° to 400° (medium-high) heat. Grate zest from lemons to equal 1 Tbsp. Cut lemons in half; squeeze juice from lemons into a measuring cup to equal 1/4 cup.
2. Whisk together lemon zest, lemon juice, garlic, next 3 ingredients, and 1 tsp. salt. Reserve 1/4 cup lemon mixture. Pour remaining lemon mixture in a large zip-top plastic freezer bag; add chicken. Seal and chill 15 minutes, turning once. Remove chicken from marinade, discarding marinade.
3. Brush corn with 1 Tbsp. olive oil; sprinkle with remaining 1/2 tsp. salt.
4. Grill chicken and corn at the same time, covered with grill lid, 20 minutes, turning chicken once and turning corn every 4 to 5 minutes. Remove chicken, and cover. Hold each grilled cob upright on a cutting board, and carefully cut downward, cutting kernels from cob.
5. Stir together cornbread mix and 2/3 cup water in a small bowl until smooth. Stir in basil and 1 cup grilled corn kernels. Pour about 1/4 cup batter for each corn cake onto a hot, lightly greased griddle. Cook cakes 3 to 4 minutes or until tops are covered with bubbles and edges look dry and cooked; turn and cook other side.
6. Thinly slice chicken. To serve, place 2 corn cakes on each plate, top with chicken and 2 bacon slices. Toss arugula with reserved lemon mixture. Place arugula on bacon, and sprinkle with corn kernels.