Psalm 11 is so fitting when a Christian feels like society and its values are just dominating so hard that many feel like throwing in the towel. The center verse says, "Yahweh is in his holy temple. Yahweh, his throne is in the heavens." Remember, heaven is primarily seen as God's command center, and as our gracious and sovereign ruler, nothing escapes his attention as he is interested in what's going on below. I think of Hebrew 4:13.
Psalm 12 has the theme of proud words versus pure words. There were so times in David's life for which this Psalm would've been quite appropriate. I think of the Ziphites while David was fleeing Saul (1 Samuel 23) or deceitful traitors like Ahithophel during Absalom's coup (2 Samuel 16-17).
Smooth lies include times when we try rationalize or explain away sin saying, "Everybody's doing it." Or "it just feels right." And of course, God's Word is the antidote to such thoughts, and the Lord will protect and guard us as we guard and protect his Word. I imagine this Psalm was so appropriate, comforting, and treasured by the early Christians as they faced persecution form the sake of God's Word and confessing Jesus as Lord.
I'm really enjoying making the Psalms the basis of my prayer life...it should've been obvious, but that's how it goes sometimes.