A couple of relevant theological questions:
1. Is it okay to pray for the souls of the dead, e.g. my father?
Answer: Yes. We can certainly pray for the souls of the living. That is, we can pray that it is God’s will that He has chosen them for heaven. We can pray for them no matter how wicked they are or how imperfect their faith in God. We can pray not only that they change their behavior or belief, but that God will have mercy on them despite their sins. Indeed, we all need that mercy and should pray for it for ourselves; we all sin, and it is just a matter of degree.
God is not stuck in time as we are. He has a plan, and we pray even though He has that plan and knows what will happen anyway. Thus, it is fine to pray even if something has already happened. If we hear of a plane accident, we can pray that our friend on the plane has survived, even though at the time of our prayer he is already either killed or not.
Thus, we can also pray for the soul of someone who has already died. We can pray either that he had a deathbed conversion or that even if he didn’t, God will be (was? is?) merciful.
2. Is it okay to ask a dead person, e.g., my daughter Elizabeth, to pray for me?
Answer: I don’t know. This came up because a lady asked me if she could pray to Elizabeth to pray for her. This is what Eastern Orthodox and Roman Catholic people are supposed to do when they pray to saints. (What commonly happens is that they pray to the saint directly— “Please cure my cancer” as opposed to “Please pray to God to cure my cancer”— but it is properly considered idolatry to make direct requests, I think.)
It is wrong to ask someone to pray for me on the grounds that they have special clout with God because they are especially holy. The Roman Catholic doctrine that saints have superogatory merit that they can give away to the rest of us as a sort of spiritual cash is an evil doctrine. Saints are, we may hope, members of God’s elect, but not on account of their special virtue, nor do they have special power with Him. My Lizzie was especially spiritual, and gave more evidence than the vast majority of us of being one of God’s children, but she was a sinner too, and showed it in daily life.
Nonetheless, it is good to ask fellow Christians to pray for us, and Lizzie is a fellow Christian, even though she is dead. So, is it proper to ask her to pray for us now, not as a special saint, but as a saint such as we hope we are ourselves? I don’t know.