Dear Shweta,
"Leave" with its classification into several kinds, in general, is a welfare measure enabling an employee to be away from the place of work with the authorization of the employer, mostly with salary and at times without salary, so as to have no negative effect on his/her continuity of service. Therefore, the classification of leave into different kinds is an arrangement to avail this benefit based on the circumstantial necessities of the individual employee.
Leave like casual leave and sick leave has no cumulative effect, and they get lapsed in the calendar year itself, whereas earned leave has a cumulative effect, i.e., carrying forward of the unavailed days to the succeeding years subject to a certain limit and is encashable in the event of termination of employment. Therefore, there would be the tendency in the employees to avail of the CL and SL first and take EL only in the case of their exhaustion.
If the leave accounts of the employees are managed up to date and the balance of the leave position is conveyed to the employees periodically, the situation described in your post would have been avoided by the employee himself by specifically applying for EL. Anyway, there is no harm in asking the employee to submit a revised leave application for EL and sanction it, or you can sanction EL suo moto mentioning the fact of exhaustion of other leaves at credit instead of straight away treating it as LOP, which may be a practical and flexible Leave Policy as well as a good HR Practice.