The Lord liveth - Yahweh - the name used here - is often described as the living God in contradistinction to idols, who are represented as without life, Deuteronomy 5:26; Joshua 3:10; 2 Kings 19:4; Psalms 42:2; Matthew 16:16; 1 Thessalonians 1:9. Compare Psalms 115:5; Psalms 135:16. It is probably in allusion to this idea that the phrase “The Lord liveth” is used here. It is a joyful exclamation in view of all that God had done; of all the deliverances which he had performed for the author of the psalm. In the remembrance of all this the psalmist says that God had shown himself to be the living, that is, the true God. These interpositions furnished abundant demonstration that Yahweh existed, and that he was worthy of adoration and praise as the true God. So, in view of mercy and salvation, the heart of the redeemed exultingly exclaims, “The Lord lives - there is a living God.”
And blessed be my Rock - God, who has shown himself to be a refuge and a protector. See the note at Psalms 18:2.
And let the God of my salvation be exalted - The God who has saved me from my enemies. Let him be exalted, be praised, be honored, be adored. Let his name be exalted above all idol gods; above all the creatures that he has made. The wish is, that His name might be made prominent; that all creatures might praise and honor Him.