David does not mince words when it comes to talking to God about his enemies. Whatever David was dealing with, it was so painful to him that he wished horrible things upon those who opposed him. He asks God to bring the lies of his attackers down on their heads (7:15-16).
The principle we learn from Scripture regarding enemies who oppose truth and want to harm us is this: we are to love what God loves and hate what He hates. We can't judge another man's salvation but we can and ought to judge his behavior. In these verses, David is asking God to eternally judge the behavior of those who through their actions are opposing God's will for the nation of Israel.
When David prays in verse 10, "Let burning coals fall upon them", he is probably recalling the judgment of Sodom and Gomorrah (Genesis 19:12-29).
David is telling God how these people have hurt him and have sought to disrupt and destroy the plans of God. Although God knows all things as we have noted in previous verses, David is giving the situation to God and in effect saying, "Dear God, this is Your problem. You deal with it".