This is the family-relationship between the tribrid-doppelgänger, Alexandria Gilbert and the siphoner, Lizzie Saltzman.
They became step-sisters though Alaric still technically being married to Isobel as he haven't finished the wedding he and Jo had. Since Alex sees Caroline as a sister she considers Lizzie as her niece than step-sister, but loves her all the same.
During Season Eight of The Vampire Diaries, Alex raises her kids as Alaric and Caroline raised their daughters. Due to Damon Salvatore under Sybil's influence all the kids were in danger once again. Kai Parker returns after Sybil is put down and goes after Josie, Lizzie, Alex's children, and Lia. After Stefan's death, Alex gave 10 million dollars to help start up the Salvatore Boarding School and said she'll be back after she finds a way to wake up the Mikaelson's.
In Season One of Legacies, Alex is the female figure that Lizzie goes to for advice when she can't reach her mother or someone to talk to when she's sad or about to have an episode. She always has time for Lizzie if she needed her aunt while taking care of her kids, and being Headmistress.