You plugged in E=279 kJ. But you are dealing with the energy of removing one electron from the atom. The context of your units is wrong. The units of a number tell you what it is you are talking about.
In this case, consider: E=hf. For E, is there a difference between plugging in E=279 kJ and plugging in E=279 kJ/mol?
In the first case, you are plugging in a flat amount of energy, 279 kJ.
In the second case, you are using the amount of energy necessary to remove a mol of electrons from Lithium.
These are the same amounts of energies, but there is an immediately apparent contextual significance.
Now is the question asking you for the minimum energy involved in removing a mole of electrons?
Also, the question asks for the complete removal of the electron, without mentioning anything about energy levels. You shouldn't need to worry about the Rydberg formula (Bohr model equation as you called it). The question is simply asking for the light's relationship of wavelength to energy.