The term 'sacrifice of praise' which is used in Psalm 49/50:14 and also in Hebrews 13:15 ("Through [Jesus] then let us continually offer up a sacrifice of praise to God, that is, the fruit of lips that acknowledge his name"), has since from early on apparently been applied to the Eucharist. To quote the Catechism, paragraph 1359: "The Eucharist, the sacrament of our salvation accomplished by Christ on the cross, is also a sacrifice of praise in thanksgiving for the work of creation. In the Eucharistic sacrifice the whole of creation loved by God is presented to the Father through the death and the Resurrection of Christ. Through Christ the Church can offer the sacrifice of praise in thanksgiving for all that God has made good, beautiful, and just in creation and in humanity."
Aside from the Byzantine liturgy, we can see it referenced within the Roman Canon at the commemoration of the living - which is what I was also thinking of when trying to come up with a title for this blog:
Memento, Domine, famulorum, famularumque tuarum N. et N. et omnium circumstantium, quorum tibi fides cognita est, et nota devotio, pro quibus tibi offerimus: vel qui tibi offerunt hoc sacrificium laudis, pro se, suisque omnibus: pro redemptione animarum suarum, pro spe salutis et incolumitatis suae: tibique reddunt vota sua aeterno Deo, vivo et vero.We go to Ἔλεον εἰρήνης. As we have noted, this phrase literally translates to "mercy of peace," which admittedly does not make much sense, to the point that some who use an English translation of the Divine Liturgy soften it into more comprehensible forms like "Offering of peace" or "mercy and peace". There have been various attempts to explain what the original wording could have been (there are have apparently quite a number of variants throughout history). For all intents and purposes, I chose to preserve the textus receptus version here. After all, εἰρήνης (pronounced as irinis in Byzantine Greek) is a good rhyme to laudis. ;)
Remember, Lord, your servant men and women (Names) and all here present. You are aware of their faith and know their devotedness. We offer for them, or they offer, this sacrifice of praise for themselves and all who are theirs, for the redemption of their souls, for the hope of their health/salvation and safety; and they present their prayers to you, the eternal, living, and true God.