Both destinations are served by Lucknow (LKO). Since there's no flight route between them, the best way to travel is by road.
Farrukhabad
Fly to Lucknow (LKO), then travel by road to Farrukhabad. Taxis, buses, and private cabs are available from the airport.
Lakhimpur Kheri
Fly to Lucknow (LKO), then travel by road to Lakhimpur Kheri. Local transport options include taxis, auto-rickshaws, and state buses.