There are directories for listed land line numbers but unfortunately there is no free directories where you can reverse lookup an unpublished phone number for free. Sri-Lanka Mobile Database This is because this type of phone numbers are regarded as private properties and the details behind them are not listed on public or free directories.

This simply means you can not lookup an unpublished number on free directories such as and the like. That does not however mean you can not locate an unpublished phone number for free, what it means if that you will have to take a different approach in order to find the information you need.
One good approach you can use to locate an unpublished phone number for free is to search the said number on internet search engines such as Google. This method works but it depends largely on if the owner of the unpublished number has ever previously listed his or her number any where on the internet.