Is there any possibility to find my father's lost iPhone?
Using a Apple ID along with Find my iPhone it could have been located if it set up with a iCloud account.

If the device was not set up with an iCloud account, the only recourse is to keep calling it in the hopes some honest person will answer.

However, there is no way to track it without the Apple ID.


  Requirements 
  
  As of January 2013, the service is supported on
  iPhone, iPad, iPod Touch, and Mac computers running OS X 10.7.5 "Lion"
  or later. In addition to a compatible device, a free iCloud
  account is required to use Find My iPhone. Users can also track
  their Find My iPhone enabled devices through iCloud.com on Windows,
  but cannot use it the other way around to track their PC.