Paul wrote:
1 Timothy 2:1-4 King James Version (KJV)
2 I exhort therefore, that, first of all, supplications, prayers, intercessions, and giving of thanks, be made for all men;
2 For kings, and for all that are in authority; that we may lead a quiet and peaceable life in all godliness and honesty.
3 For this is good and acceptable in the sight of God our Saviour;
4 Who will have all men to be saved, and to come unto the knowledge of the truth.
I believe it is our duty to pray for the salvation of all men. Even those whom we might believe didn't receive the fullness of divine truth. In this, we pray for them while they are alive, praying that they come into the full knowledge of the truth and be saved. For those who came only so far, I believe that we continue to pray that they receive greater understanding. And those who perish in that state, I believe in praying that God has mercy upon them. And at that point, the book is closed. At that point, it is in the hands of God. And I believe that whatever judgment God makes concerning a soul in the judgment is righteous, just, and true. It's my last and final prayer of intercession for those who I know are in desperate need of a sovereign grace.
It is also evangelistic. For many "Christians" were deeply touched in their lives by Billy Graham. But praying for God to have mercy on the man, and leaving it in the hands of God, I leave doors open to win those who, like him, don't have the fullness of truth. But... if they read my arrogant words of condemnation, professing that Graham busted Hell wide open, that Graham was lost without hope, that he was a heretic, that he hasn't a snow ball's chance in Hell, etc., etc.... I know that my words will appall them. And my attitude and spirit will cause many of them to write me off before they've heard anything I have to say. I have family members who were touched by Billy Graham's ministry. Do you think they'll receive anything I have to say if I vehemently proclaim that I believe Billy Graham is burning in Hell???
Praying a final intercessory prayer, for a sovereign move of God's grace, isn't a sin. It is actually reveals the character and desire of the heart of that individual praying said prayer. It testifies that he or she desires all men to be saved. It testifies to that individual's trust and belief in God's sovereignty. And it testifies to their unwillingness to make eternal judgments based on outward appearances. To me, I believe it reflects a greater spiritual maturity than the spitting and fussing spirit that insists with clinched fists that someone is burning in Hell because they "followeth not us".