Is it permissible to lie to a female relative who requested money and did not return it, under the pretext of recovering the money she did not return?

It is not permissible to lie in this situation. One can resort to tawriyah and ma'areedh, which involve using general words that the listener understands to mean something other than what the speaker intends. Lying is forbidden except in cases of necessity or extreme need, where no other legitimate means exist. Ma'areedh is a legitimate means that does not fall under lying, as a word is used that carries two meanings, and the speaker intends a correct meaning while the listener understands another meaning. For example, one can say: "I do not have money," and the speaker intends money that is in excess of their needs.