Marrying into the Lockwood family
Lydia married Ben and together they had a son named George. She was shown responding to her father-in-law, Peter Lockwood, regarding his anti-alien comments; stating that he is not to speak that way in their house. Her husband, Ben, originally had a neutral viewpoint about aliens; only to become anti-alien himself due to his father's death, which led him to become Agent Liberty.
Discovering that Ben is Agent Liberty and supporting him
Lydia originally was unaware of her husband's activities until he was arrested and publicly revealed as Agent Liberty. She and George were shown alongside Ben after he was released from prison; and later on, Lydia became an anti-alien bigot herself, informing George that Ben was saving humans as Agent Liberty.
Later, Ben and his Children of Liberty began to arrest innocent aliens and she approved of the anti-alien propaganda. Lydia was killed by a female alien who's husband was wrongfully arrested by the Children of Liberty, in retaliation for Ben's actions.
In an attempt to fix her relationship with Lena Luthor, Kara and Mxyzptlk created a timeline in which instead of hating aliens, Lydia worshiped Kara Zor-El and with her father in law and her son, they joined the Cult of Rao. She, along with her son and her father in law, died in a botched attempt to get Supergirl to save them by jumping off of a roof.
Despite the fact that George Lockwood had become disgusted with Lydia's propaganda towards aliens (after he discovered that one of his friends is an alien) he still had some respect and love left for his mother, as he attended her funeral, after she was murdered by an alien in retaliation for her husband who was wrongfully arrested by the Children of Liberty.
Lydia's death caused George to see how Ben Lockwood's vendetta towards aliens has caused their family's suffering and cut all ties with his father, blaming him for his mother's death.
Lydia was devoted to her family and loved them very much. Despite her father-in-law, Peter Lockwood, being pessimistic, she never kicked him out of the house.
It was unknown what Lydia's stance on aliens originally was, but after her husband, Ben Lockwood got arrested when his identity as Agent Liberty was finally exposed, she became pro liberty and anti-aliens.