Hi,
No one can accept the late because he worked for late hours in the previous day. It is the responsibility of the employee to complete his work on daily basic. So it is not correct to accept that reason. You can implement late coming policy for your company.
Sample policy : Late coming is permitted till--- AM, if employee is coming after--- AM, then it would be considered as late arrival, and ---- late arrivals in a month will be considered as a one half day personnel leave.
You can implement according to your management acceptance for the same.