Now this is an interesting question.  Basically the question is asking can the dead who were lost after this life be helped by something that we ourselves do.  The Bible teaches plainly that a person is responsible for his own soul, i.e. personal responsibility (Ezekiel 18:4,20; Galatians 3:26,27; II Timothy 2:19).  Luke 16:19-31 teaches that once a person is dead his fate is sealed, and no where in the pages of the Bible is such intercession or action made.
    The Mormons for example believe, “When any of you are baptized for your dead . . .” (Joseph Smith in Doctrines and Covenants) that such “proxy baptism” will lead to salvation, but Mark 16:16a says “He that believeth and is baptized shall be saved.”  Who?  That one who was so immersed.  Not the one who was the object of the immersion by he who had been immersed for he who had not been immersed (try saying that ten times fast).
    Similar to this doctrine is the Catholic doctrine of “necrologies,” and this gets us to our actual question:  “Can we pray for the dead?”  I quote the Catholic Encyclopedia, “Necrologies . . . are the registers in which religious communities were accustomed to enter the names of the dead—notably their own deceased members, their associates, and their principal benefactors—with a view to the offering of prayers for their souls.”  In fact often such was used as “a constant subject of negotiation between different abbeys,” or if a service was granted, “requesting the promise of prayers . . . for the deceased brethren of the monasteries who rendered them this service.”  (Let alone that these were praying for those whose fates had been sealed what kind of motives were behind such?  Sounds like these prayers for the dead were self motivated:  Often these were benefactors, or the prayers were offered to secure favors from neighboring abbeys or monasteries.
    Perhaps we should follow Jesus’ model for prayer (Matthew 6:12) and pray that he will forgive what we owe as we forgive those who are debtors to us.  Hebrews 9:27 reads, “And as it is appointed unto men once to die, but after this the judgment.”  That is speaking sequentially and does not make allowance for works of the living aiding the dead.