{{___ Where does the Bible teach innate immortality?}}
You are correct. The Bible does not teach "innate immortality".
Immortality, eternal life, is a free gift to the born again on the basis of unmerited favor and through the instrument of supernatural faith in the Resurrection and in one's own eternal salvation through the blood sacrifice of the Son.
On the other hand, some persistence of the remains of the individual who decides (generally, through culpable neglect, perhaps) to spend eternity without God is indicated in scripture. The texts are familiar.
I follow C. S. Lewis on the notion that what remains of the lost individual in eternity is miniscule and is totally evil. All in the present existence is supported and maintained by the presence of God.
Acts 17:28 KJV For in him we live, and move, and have our being; as certain also of your own poets have said, For we are also his offspring.
The lake of fire would seem to be a place where all the good that God ordinarily provides to His creatures is not present.
It is not unreasonable to think that Jesus was spiritually in the lake of fire when on the Cross:
Matthew 27:46 KJV And about the ninth hour Jesus cried with a loud voice, saying, Eli, Eli, lama sabachthani? that is to say, My God, my God, why hast thou forsaken me?
One can even go further and consider that the lake of fire was created at this time. It was necessary that there be a creation without the normal presence of God. Jesus had become sin and a curse. And yet His spiritual fellowship with the other Persons could not be broken without the creation of a special place.
{{___ Why seek for immortality if one already has it?}}
Psalms 62:12 LITV Also mercy belongs to You, O Lord, for You reward a man according to his work.
Romans 2:6-10 LITV He "will give to each according to his works:" LXX-Psa. 61:13; MT-Psa. 62:12 (7) everlasting life truly to those who with patience in good work [are] seeking glory and honor and incorruptibility; (8) but to the ones truly disobeying the truth out of self-interest, and obeying unrighteousness, will be anger and wrath, (9) trouble and pain on every soul of man that works out evil, both of Jew first, and of Greek. (10) But glory and honor and peace will be to everyone working out good, both to the Jew first, and to the Greek.
Rightly translated and interpreted this passage has much to say about the present evidence of right and wrong behavior, and of present evidence of eternal blessing. Seeking to minimize the effects of mortality, that is the weakness and corruption of the flesh is a worthwhile endeavor.
We must interpret this passage in terms of others which plainly show that the seeking of glory and honor and incorruptibility through endurance of good works is a mark of the born again and of the already irrevocably given eternal life.
