I will praise thee, O Lord ... - This is taken from Psalms 57:9. The only change is the substitution here of the name יהוה Yahweh for אדני 'Adonāy. Why that change was made is unknown.
Related Commentaries of Psalms 108:3
Psalms 108:3
3 I will praise thee, O LORD, among the people: and I will sing praises unto thee among the nations.