Lailas friendship with Mariam begins when she defends Mariam from a beating by Rasheed.
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She completely disapproves of Rasheed's behavior since he has already dealt with Mariam cruelly. He is angry that Mariam has not "given" him a son and demonstrates over and over again that he is sadistic in his treatment of his women, especially Mariam whose pregnancy has resulted in the birth of a daughter. Laila has simply had enough and refuses to let such cruelty go on.
Mariam had been abused and neglected by Rasheed herself. She didn't want Rasheed to take another wife, but she also feels protective of Laila, and she often passes Laila off as her daughter. There is a kinship between them, forged by Rasheed's abuse.