make an entry at the police station. Then with a copy of the entry (make sure to get the entry number), go to your Grama Niladari (ග්රාම නිලධාරී) and request a for a new NIC. Say that you want the one day service. Fill the form, along with photos, get the Grama to sign it and hand over to the ID office at Jawaththa Road, for same day service. Make sure you hand it in the morning and you'll get it same day evening. (Anywhere from 3.30 pm to 6.00 pm )
edit:
for same day service you need to pay some money.