Is it permissible to lie to one's father to conceal dropping out of college due to its temptations, knowing that the mother is aware, and fearing the father's anger and punishment, and desiring to seek religious knowledge?

Studying in mixed-gender universities is not permissible except out of necessity or need. Nevertheless, one must strive to fulfill the father's wish out of righteousness towards him, such as searching for another university, or continuing while avoiding mixing and its temptations, and being keen on the company of righteous people. If you do not feel safe from temptation, try to convince your father through the mediation of good people. Lying is forbidden except out of necessity or a religiously recognized benefit. One should limit oneself to dissimulation (tawriyah) and allusive speech (ma'arid). It has become easy to acquire Islamic knowledge online in our time.