What is the Islamic ruling on the son's action of not informing his sick father of his approaching death? Does this align with Islamic law and religion, or should he have informed him so that he could repent and prepare to meet his Lord?

The default is that obedience to one's father is obligatory. However, if there is a fear that informing a psychologically ill father about the reality of his serious illness would worsen his condition, then there is no harm in not informing him. In fact, it is wise to conceal the matter from him and to strive to comfort him, because informing him would increase his anxiety, despair, and despondency. Especially since Islamic law mandates alleviating the burden on the sick, not saddening them. What is desired from his will, seeking forgiveness, and preparing for death can be achieved by encouraging him to write his will and by encouraging him to draw closer to Allah through good deeds, settling debts, and fulfilling obligations. These are matters required of every person, whether healthy or ill.