Countess Lydia is respected in Petersburg society as a pious do-gooder, but she's also a total hypocrite. She claims to be a good Christian, but she uses her religion to prove that people who accept God into their hearts are automatically better than anyone else around them. She uses this to prove that Karenin is some kind of paragon of virtue after he breaks off relations with Anna. To Countess Lydia, Karenin is a hero, and Anna is a demon.
Countess Lydia's smug, complacent, and self-serving view of religion and the world authorizes her to do one of the worst things in the novel: she tries to prevent Anna from seeing her own son, Seryozha, and she tells the boy that his mother is dead. Anna's got her own issues with children (see her "Character Analysis" on this), but Countess Lydia still has no right to be interfering in the relationship between Seryozha and Anna.
Countess Lydia's an interfering old society lady, as bad as Princess Betsy in her way. In some ways, Countess Lydia takes advantage of Karenin's vulnerability to come between him and Anna, and effectively prevent any resolution that would benefit Anna. Countess Lydia makes it impossible for Karenin to hang on to his religious epiphany, or for Anna to reestablish any kind of normal relationship with Seryozha or Karenin. Society, whether religious (as in Countess Lydia's case) or immoral (as in Princess Betsy's case), continues to be the bad guy in keeping people from behaving as their instincts tell them to.