The daily prayer for forgiveness is nothing other than the humbling cry for forgiveness, "God, be merciful to me, a sinner!" (Luke 18:9-14, ESV). As Luther put it,
For what is our prayer but a confession that we neither have nor do what we ought and a plea for grace and a happy conscience? This kind of confession should and must take place incessantly as long as we live. For this is the essence of a genuinely Christian life, to acknowledge that we are sinners and to pray for grace. [Martin Luther, Preface to the Large Catechism, 1529 revised edition. Tappert, T. G. (2000, c1959). The Book of Concord: The Confessions of the Evangelical Lutheran Church. Philadelphia: Fortress Press.]
Even the petition for bread is a plea for grace, for in it we pray we would have enough to keep us from falling into mortal sin but not so much that our faith is undermined (Proverbs 30:8-9; cf. David Scaer, Discourses in Matthew). Since prayer is a plea for grace, it has God’s promise of grace, which is why doubting that one will receive the things requested accuses God of breaking his word:
Thus God has briefly placed before us all the distress which may ever come upon us, so that we might have no excuse whatever for not praying. But all depends upon this, that we learn also to say Amen, that is, that we do not doubt that our prayer is surely heard, and [what we pray] shall be done. For this is nothing else than the word of undoubting faith, which does not pray at a venture, but knows that God does not lie to him, since He has promised to grant it. Therefore, where there is no such faith, there cannot be true prayer either. [Martin Luther, Part III of the Large Catechism, emphasis added]
Addendum
That is why Luther’s Large Catechism, in its conclusion to the Ten Commandments, says the Lord’s prayer would not be needed by those who perfectly keep them.
The prayer does not exclude praying that others come to faith: Jesus sometimes healed by the faith of a third party.