Is it permissible to lie to the wasteful husband to save money for the family, by claiming to have borrowed it from others, knowing that the money is not wasted on unlawful matters but is used to help the family?

Lying is forbidden and leads to immorality and Hellfire, so a Muslim must avoid it. What you mentioned about your husband's extravagance does not justify your lying. Rather, you should advise him and remind him of the prohibition of extravagance. Allah Almighty says: "Indeed, the wasteful are brothers of the devils, and ever has Satan been to his Lord ungrateful" (Al-Isra: 27). If he persists in his extravagance, there is no harm in using allusive speech (tawriya) and ambiguous statements (ma'arid) to take money and spend it on the family's needs. A woman may take from her husband's wealth, within reasonable limits, what suffices her and her child if he withholds it from her, and she may use stratagems to obtain her right. However, if he fulfills her right, it is not permissible for her to take from his money except with his permission and his willing consent.