The Bible itself provides little, if any, explicit guidance on what it is that we are to ask God to do when we ask him to save someone. That we are to pray, no one disputes. That we are to pray for the lost to be saved, no one denies. Jesus does not pray for people to believe but for the unity of those who will believe through the evangelistic word of those who already believe (see John 17:20-21). Paul’s grief for lost souls is intensely sincere (Rom. 9:1-5), and his ‘heart’s desire’ and ‘prayer to God for them’ is for their “salvation” (Rom. 10:1; see also his admonition in 1 Timothy 2:1-2 that ‘prayers’ and ‘petitions’ be offered up on behalf of ‘all men’). His advice to Timothy that he ‘with gentleness’ correct those in opposition is made on the grounds that ‘perhaps God may grant them repentance’ (2 Tim. 2:25). The problem is that in none of these instances is it specified what we are to ask or petition God to do in the heart of an unbeliever.
You pray for the conversion of others. In what terms, now, do you intercede for them? Do you limit yourself to asking that God will bring them to a point where they can save themselves, independently of Him? I do not think you do. I think that what you do is to pray in categorical terms that God will, quite simply and decisively, save them: that He will open the eyes of their understanding, soften their hard hearts, renew their natures, and move their wills to receive the Saviour. You ask God to work in them everything necessary for their salvation. You would not dream of making it a point in your prayer that you are not asking God actually to bring them to faith, because you recognize that that is something He cannot do. Nothing of the sort!
When you pray for unconverted people, you do so on the assumption that it is in God’s power to bring them to faith. You entreat Him to do that very thing, and your confidence in asking rests upon the certainty that He is able to do what you ask.
And so indeed He is: this conviction, which animates your intercessions, is God’s own truth, written on your heart by the Holy Spirit. In prayer, then (and the Christian is at his sanest and wisest when he prays), you know that it is God who saves men; you know that what makes men turn to God is God’s own gracious work of drawing them to Himself; and the content of your prayers is determined by this knowledge. Thus by your practice of intercession, no less than by giving thanks for your conversion, you acknowledge and confess the sovereignty of God’s grace. And so do all Christian people everywhere.’
Adopted from monergism.com and Sam Storms
So how are we to pray for the unbeliever knowing that God is the one who brings about salvation of those who are lost.