Through him, then, let’s offer up a sacrifice of praise to God continually, that is, the fruit of lips which proclaim allegiance to his name.
Notice the two words the writer uses for what comes out of our mouths. Fruit, and lips. Praise here is not described as a mood or an inner state. It is something spoken, and it grows out of a life the way fruit grows out of a tree.
He also calls it a sacrifice, which tells us it will sometimes cost us. And he says it is offered through him, which tells us where the worthiness of the offering comes from. Not from the quality of our week, and not from how sincerely we feel it.
Then there is that last phrase, allegiance to his name. That is a stronger claim than saying pleasant things about God. It is the public alignment of a person with the One they belong to, spoken out loud, in the hearing of a world that has other names on offer.