Both Andromeda and Sirius were burned off the Black family tree tapestry at their ancestral home at 12 Grimmauld Place.
Bellatrix hates Sirius because he ran away from home and is a 'blood traitor', since he doesn't hate non-pure-bloods. Bellatrix stopped talking to Andromeda when she married the Muggle-born wizard Ted Tonks, and the Black family as a whole disowned Andromeda. Obviously, she doesn't get along with Andromeda Tonks or Sirius Black. Bellatrix took the name Lestrange when she married Rodolphus Lestrange (likely a descendent of Leda Lestrange from Fantastic Beasts and Where to Find Them) Sirius Black is Bellatrix' paternal first cousin, and so is his brother, the former Death Eater Regulus Black.
Her sisters are Narcissa Malfoy (Lucius Malfoy's wife and Draco Malfoy's mother) and Andromeda Tonks- mother of Nymphadora Tonks, who married Remus Lupin. Her father and mother were Cygnus Black III and Druella Black (née Rosier). Bellatrix Lestrange was born Bellatrix Black.
