Objection 1. It would seem that God should not be praised with the lips. The Philosopher says (Ethic. 1,12): "The best of men ere accorded not praise, but something greater." But God transcends the very best of all things. Therefore God ought to be given, not praise, but something greater than praise: wherefore He is said (Sirach 43:33) to be "above all praise."
Objection 2. Further, divine praise is part of divine worship, for it is an act of religion. Now God is worshiped with the mind rather than with the lips: wherefore our Lord quoted against certain ones the words of Isaiah 29:13, "This people... honors [Vulgate: 'glorifies'] Me with their lips, but their heart is far from Me." Therefore the praise of God lies in the heart rather than on the lips.
Objection 3. Further, men are praised with the lips that they may be encouraged to do better: since just as being praised makes the wicked proud, so does it incite the good to better things. Wherefore it is written (Proverbs 27:21): "As silver is tried in the fining-pot... so a man is tried by the mouth of him that praiseth." But God is not incited to better things by man's words, both because He is unchangeable, and because He is supremely good, and it is not possible for Him to grow better. Therefore God should not be praised with the lips.
On the contrary, It is written (Psalm 62:6): "My mouth shall praise Thee with joyful lips."
I answer that, We use words, in speaking to God, for one reason, and in speaking to man, for another reason. For when speaking to man we use words in order to tell him our thoughts which are unknown to him. Wherefore we praise a man with our lips, in order that he or others may learn that we have a good opinion of him: so that in consequence we may incite him to yet better things; and that we may induce others, who hear him praised, to think well of him, to reverence him, and to imitate him. On the other hand we employ words, in speaking to God, not indeed to make known our thoughts to Him Who is the searcher of hearts, but that we may bring ourselves and our hearers to reverence Him.
Consequently we need to praise God with our lips, not indeed for His sake, but for our own sake; since by praising Him our devotion is aroused towards Him, according to Psalm 49:23: "The sacrifice of praise shall glorify Me, and there is the way by which I will show him the salvation of God." And forasmuch as man, by praising God, ascends in his affections to God, by so much is he withdrawn from things opposed to God, according to Isaiah 48:9, "For My praise I will bridle thee lest thou shouldst perish." The praise of the lips is also profitable to others by inciting their affections towards God, wherefore it is written (Psalm 33:2): "His praise shall always be in my mouth," and farther on: "Let the meek hear and rejoice. O magnify the Lord with me."
Reply to Objection 1. We may speak of God in two ways. First, with regard to His essence; and thus, since He is incomprehensible and ineffable, He is above all praise. On this respect we owe Him reverence and the honor of latria; wherefore Psalm 64:2 is rendered by Jerome in his Psalter [Translated from the Hebrew]: "Praise to Thee is speechless, O God," as regards the first, and as to the second, "A vow shall be paid to Thee." Secondly, we may speak of God as to His effects which are ordained for our good. On this respect we owe Him praise; wherefore it is written (Isaiah 63:7): "I will remember the tender mercies of the Lord, the praise of the Lord for all the things that the Lord hath bestowed upon us." Again, Dionysius says (Div. Nom. 1): "Thou wilt find that all the sacred hymns," i.e. divine praises "of the sacred writers, are directed respectively to the Blessed Processions of the Thearchy," i.e. of the Godhead, "showing forth and praising the names of God."
Reply to Objection 2. It profits one nothing to praise with the lips if one praise not with the heart. For the heart speaks God's praises when it fervently recalls "the glorious things of His works" [Cf. Sirach 17:7-8. Yet the outward praise of the lips avails to arouse the inward fervor of those who praise, and to incite others to praise God, as stated above.
Reply to Objection 3. We praise God, not for His benefit, but for ours as stated.
Source: Summa Theologica (New Advent)