What if your birth certificate doesn't have City? It only has province and division.
On my naturalized passport I have place of birth as my province. When I filled the DV form I put the province as City of birth.
Could this be a problem?
This could be a problem because you filled in your DV application inaccurately. Regardless if your Birth Certificate mention the city of your birth or not, a province is still a province, and not a city.
You should have put the name of the City of your birth when it asked for the name of the city instead of the name of the province because when you get selected, on the DS-230 form that you will have to send back to KCC, it will asked for "City of Birth" and it will also ask the "Province" in a separate questions.
What is the country of birth in question here?
Sri Lanka is a good country, very beautiful also. Why you want to migrate to USA ?
Where is your interview? If it is in Sri Lanka they may know the province name and city name, but if it is in canada or us then consular is less likely to google the name of provinces of sri lanka before your interview.