The central irony in The Lady with the Pet Dog by Joyce Carol Oates is a situational irony. This means that a situation in the story is expected to be one thing or turn out one way and is in fact another thing or in fact turns out another way. For instance say you loath performer X and refuse to go to his concerts but one day discover that Local Band Q is opening for Performer X and so you run out and buy a front row ticket. This is situational irony: Since you loath X, we expect you to shun the concert but you buy a front row seat ticket. the irony would be heightened if, after staying through the whole concert, if for no ohter reason than to get your money's worth, you actually liked X's performance!
The situational irony in The Lady with the Pet Dog revolves around the fact that Anna is feeling nearly fatally miserable because she is in an unhappy marriage and in love with a married with a blind child who will never divorce his wife. Anna despairs because she loves this married man with whom she is having an affair and there is no way to find an ending that gives her happiness and freedom from a marriage that makes her feel like "nothing." One day Anna has an epiphany (great realization) and understands that she can stop thinking of her affair as something wrong with her life and something that is keeping her from happiness and start thinking of it as a true marriage of happiness. This is an outcome that neither she nor the other man was expecting. It is situational irony: An affair that is condemned, that shows the false nothingness of her marriage, drives her to the brink of the deepest unhappiness and nearly drives her to ending her life becomes her true marriage of happiness.