Is this a playable race? All dialog is inaccessible to non playable races. The shortest way to restore their access to the dialogue is to make your race playable obviously. Some folks simply add an inclusive condition to the Imperial dialogue such as OR GetIsRace YourCustomRace == 1 the issue with doing that is it can cause conflicts with other mods that alter that dialogue quest. Another option is to make new dialogue for your race, but that can be time consuming if you want them to have voices. :foodndrink:
If you want to make your race playable, this tutorial will help: http://cs.elderscrolls.com/constwiki/index.php/Race_creation_tutorial