What is the conflict of the story "The Lady with a Dog" by Anton Chekhov?
The central conflict is the pull between loyalty and infatuation, security and the unknown, and the failure to truly know if the latter is something real or illusory. Both the man and woman are trapped in shallow lives, both seek a more satisfying relationship, a spark that makes life worth living. For example, when the pair are at dinner,
"Then both continued eating in silence, like strangers, but after dinner they walked side by side; and there sprang up between them the light jesting conversation of people who are free and satisfied, to whom it does not matter where they go or what they talk about."
However, despite these positive indications of a chance for more "alive" living, neither one is ready to give up what they know or feel comfortable with in their lives. The story concludes with a sour grapes sort of line: ""There's something pathetic about her, anyway," he thought, and fell asleep."
The conflict in "The Lady With the Dog" is that Dmitri Dmitritch Gurov is a serial philanderer who looks down on women as inferior beings he calls "the lower race," but at the same time, he cannot get along for "two days" without one. He is uncomfortable around men and finds that he is attractive to women and gets along well with them, despite his disdain for them. He finds intimacy appealing, but also notes that it rather quickly and inevitably turns into a negative complication in his life.
When he meets Anna Sergeyevna, the conflict in Dmitri's life changes; he falls in love with Anna, but neither of them are free to marry. They carry on their clandestine affair, which causes Anna great shame. Ultimately, it is not known how, if, or when the two lovers might be able to live together openly—or whether the love they feel for one another is real and enduring or merely a function of each other's unavailability.
The conflict of defining what is moral/morality is at the center of the story. Should the lovers stay with their spouses even if they do not love them, and are in love with one another?
The viewpoint seems to be that it would be wrong to live a lie and that they should leave their spouses and be together because they truly love each other.