Then read from the treasured volume The poem of thy choice,
Finally, though, after all these instructions, the speaker is going to let his reader pick "the poem of thy choice." The reader is supposed to select that poem from a "treasured volume."
Remember that "The Day is Done" poem is the preface to an anthology of poems by other authors (see "In a Nutshell"). We think that Longfellow is hoping his anthology will become a "treasured volume" full of soothing poems. He's inviting us, his readers, to read aloud from his book.
And lend to the rhyme of the poet The beauty of thy voice.
The reader and the poet team up to make the poem a soothing cure for all of our troubles. When you read aloud, the "beauty of thy voice" blends with the poem's rhythm and "rhyme" to make beautiful music.
We kind of love that image, but you've probably already guessed that we are giant poetry dorks.