Reading verses 6 and 7 in the content of the entire Psalm, we see David realizes God not only rules over this world now but He will literally rule over this world one day. Therefore, one should go through life realizing God is in charge and we are not.
The word "lowly" in verse 6 has nothing to do with one's status in life. It has to do with one's acknowledgement of the God who rules over our lives and over this world. Furthermore, the text of verse 6 says that God is "afar" from the proud. So if God is everywhere, how can the proud be "afar" from Him? This is about those who do not know God personally and those who do not trust in His guidance for their lives.
This provides the perfect transition to verse 7 which makes the point that in this life, even though we all have troubles, God is navigating our lives and guiding us against those who are "afar" from Him.
The final verse (verse 8) reminds us God will fulfill His purpose for each of his children. So if we trust God to fulfill His purpose in us, why pray like this final verse for God not to abandon us? I think the idea is simply this, 'as long as we are loyal to God, He is loyal to us.' However, we can still mess up and turn away from Him. Although God would not abandon us forever, He instead would have every right to discipline us for turning from Him. In effect, this Psalm ends with a prayer to not give up trusting God so He won't have to go to extreme measures in our lives.