Well, my Special Rockruff is female, so if I breed it with someone, the hatching Rockruff can evolve into Dusk Lycanroc?
A Rockruff with the Own Tempo will evolve into Dusk Lycanroc; it can receive this ability through breeding. Since your Rockruff is female, it will produce Rockruff offspring with an 80% chance of having Own Tempo.
Hope I helped. :)
Source (with cross-referencing)
The new Rockruff with own tempo is considered a completely new Pokemon by the game. So the offspring will have a 100% chance of having own tempo if bred with a ditto.