Literary lyrics are typically found in lyrical poetry. A lyrical poet is a poem which describes the speaker's emotions. Normally, the poem speaks of a very personal experience. The lyrical (or song) aspect of the text comes from the use of alliteration and assonance.
Alliteration is the repetition of a consonant sound within a line of poetry. Assonance, on the other hand, is the repetition of a vowel sound within a line of poetry. These poems normally contain very vivid imagery and elements of loss.
An example of a lyrical poem is Emily Dickinson's "I heard a fly buzz." The poem contains the story of the speaker's death, alliteration ("blue" and "buzz"), and the assonance of "in" and "air." When read, the poem's musical quality is apparent.