A very good question !
In my opinion, the title is about the way Lily (Susan Sarandon) "leave" this world.
Blackbirded means to leave some social place without being seen and without any goodbyes.
Here in this almost "huis clos", there's only the closest persons to Lily in this isolated manor.
Moreover, the scene just after the apparition of a black bird shows the departure of every member of the family, except Paul (Sam Neil), as if nothing happened.
