What about non-believers?
For God, who has fulfilled all that he predestines, wants us to pray for the enemies of the faith, too, so that we would in turn see that it is he who gives to the unbelievers, too, the gift of faith. And it is he who makes men who formerly were unwilling, to become men who do will it.
from St. Augustine Answers 101 Questions on Prayer by Fr. Ermatinger.
The desire of prayer is that the good things of God might be given and received by those to which they are given. Those who do not believe fall into two camps: those that do not believe because they do not know and those who know but choose to not believe. Likewise, those that are enemies of God fall into two camps: those that are enemies because they do not know what they do and those that are enemies because they know and choose to do that which is evil. The man of prayer responds to these camps in similar fashion.
God desires that we pray for our fellows, for those that are close, those who are far off, and those who are enemies that they all might receive the goodness of God, have faith, and will to do God’s will. For those who do not believe and do not act good because they do not know, the prayer is that they might know and that the good things of God might be given to them. Now for those that do not believe and do not act good because they know and yet choose to disbelieve, the prayer is the same. For those who are enemies of God, the prayer is not that evil should befall them, that they should be driven even further from God and thus act more evilly. No. Prayer for enemies is for them to have that which those who believe in God have. Surely, the prayer for those who have made themselves enemies of God might be not permitted to bring about evil and harm, but this is not the same as praying that God gives evil to His enemies, which He desires not. The task of the man of prayer is not to pray for the vengeance of the Lord, which is His alone to determine, but to pray for His goodness, His mercy, His charity, for those that seek evil that they might be won to God by His own hand.
For the truth of the matter is that all start, in one fashion or another, as unbelievers and enemies of God. It is only by prayer, of ours and of others, that God’s grace has come, one has turned, and one has believed.