Can lattice enthalpy only be determined by the Born-Haber cycle? Since we are able to determine the enthapy of formation experimentally, why it is impossible to determine the lattice enthalpy directly by experiment?
Because you can't take an ionic solid and convert it into a gas of ions. That's not a physically realistic process. You have to infer it using a Born-Haber cycle and other quantities that can be determined experimentally.