What is the ruling on a mother lying and claiming that she breastfed a girl to prevent her son from marrying her? Is she considered a liar, and what is the expiation for her lie?

Lying is fundamentally forbidden, except when it becomes the only means to avert harm that cannot otherwise be prevented. If the mother is certain that harm will befall her son in his religious practice and she cannot avert it except by lying, then there is no blame upon her and no expiation is required. The same applies if there is a significant worldly harm that cannot be avoided except through this means. However, if there is no significant harm according to Islamic law, or if there is a means to avert it without lying, then the mother is sinful and mistaken, and the expiation for this is sincere repentance. The general principle is for the son to obey his mother by not marrying someone she dislikes, unless his heart is attached to her and he fears falling into sin, in which case he prioritizes obedience to Allah over obedience to his mother.