Iris' dishonesty and secretive behavior in The Blind Assassin express the tension between her powerlessness and her attempts to regain power throughout the novel.
Her identity and her life are controlled by men, especially her father and her husband Richard. Consequently, Iris' secretive behavior is a symptom of her powerlessness and her lack of agency or choices. Because she is forced to marry Richard, whom she doesn't love, she turns to Alex for love and sexual fulfillment in a secretive affair, and this affair becomes one small way to take back her power.
Iris' secretive behavior is also a tool that she can use--perhaps one of the only tools at her disposal--to fight back against her own powerlessness and take revenge on the men in her life. Her affair with Alex becomes a kind of revenge against her father, who forced her to marry Richard. It also is a revenge against Richard, who she doesn't love and who betrays her by hiding her father's death. Similarly, the fact that she makes everyone believe the novel The Blind Assassin was written by her sister Laura is a way for Iris to preserve her sister even after Laura has died.
Also, Laura endured Richard's abuse, and Iris was powerless to stop this abuse at the time. Pretending that the novel is written by Laura is a way for Iris to give her sister some power through creating a literary legacy for her.
Thus, Iris' secretive behavior and dishonesty reflect a culture of sexism, abuse, and powerlessness, and they allow her to regain a small amount of power and agency.