How can the lattice enthalpy of an ionic NaCl be determined by using Born-Haber cycle?

Formation of NaCl may be done by two different methods:
(a) Indirect method
(b) Direct method.
(a) Indirect method: Various terms involved are:

  Since enthalpy is required for the process (endothermic), therefore  is taken as a positive quantity.
(ii) 
The process is endothermic, therefore  is taken as a positive quantity. 

Since the process is endothermic, therefore, ionisation enthalpy is taken as a positive quantity.

Since the process is exothermic, therefore electron gain enthalpy is taken as a negative quantity. 

Enthalpy is released in this process i.e. process is exothermic, therefore  is always taken as a negative quantity. 
(b) Direct method:  Let  be the enthalpy of formation of 1 mol of NaCl(s) from its constituent species. 
               
According to Hess's law, the enthalpy of formation of one mole of sodium chloride should be the same irrespective of the fact whether it takes place directly in one step.
(Direct method) or through a number of steps (Indirect method).

where  is the enthalpy change for lattice formation from
  
The reverse of the above equation i.e.
  
defines the lattice enthalpy of NaCl.
Thus by using the Born- Haber cycle,  one can determine the lattice enthalpy of an ionic compound.