while still acknowledging that it is obligatory is, according to the soundest opinion, also a disbeliever. If your father abandoned the prayer and remained in that state until he died—either never praying at all, or praying at times and neglecting it at others—then his situation is perilous, and it is impermissible to supplicate for him if he died in that condition.
As for making up the prayers, they are not to be made up, nor may anyone pray on behalf of another. It is incumbent upon every Muslim to guard his own prayer and the rest of his religion, and not to treat them lightly, lest death overtake him while he is negligent in his religion and wasteful of his prayer. Should he die in such a state, nothing will benefit him—neither supplication nor charity, Allah forbid—for he has abandoned the central pillar of Islam and has been lax concerning the most emphatic pillar of Islam after the two testimonies of faith.
In sum, if the person mentioned died upon that condition, his state is grievous—Allah’s refuge is sought—and it is not permissible for you to supplicate for him so long as he died while neglecting the prayer. Making up the prayer on his behalf will not avail him, nor will anything done for him benefit him, for he died outside the faith, if matters are as you have described and he persisted in that state without repenting before death. Allah’s help is sought.
Question: The questioner says that he was afflicted with a psychological illness that eventually led to his death, and that the condition we have described—his abandonment of the prayer and the fast, or his laziness concerning them—existed before he was struck by that illness?
Answer: That means he deliberately abandoned them without any legitimate excuse, and a psychological illness does not prevent a person from praying; one can perform the prayer even while ill. His leaving the prayer, therefore, shows a lack of desire for it.
Question: But if, during that illness, there was a loss of consciousness, for example, would he then be excused?