I claim that we should think of lyrics as an artform, and thus treat them as poetry—as the most important type of poetry, in fact. But I don’t mean that every lyric you ever write has to be a piece of genius, and you can never write anything for fun, or for practice. After all, touchdown-scoring plays are the ideal plays in football, but not every play scores a touchdown. Most plays have the job of helping you eventually get close enough to score a touchdown, just like most lyrics you write will have the job of helping you gain the ability to write artistically when you want to.
That being said, one of the things I think that separates normal poets from great poets is the recognition that every part of every line is an opportunity for artistry. The poetry doesn’t just happen at the ends of the lines. It also happens within the lines as you make strategic word choices. See, for example, the internal rhymes in C. S. Lewis’s “Narnian Suite” poems. In fact, for brilliant and inventive poetry, just read the whole Poems book by Lewis. I learned a lot simply by trying to figure out the rhyme patterns and syllable counts in his poems.
In “The True Nature of Gnomes” (read it here) for instance, Lewis uses an ABCB DEFE rhyme pattern, but also rhymes the beginning of the third line with the end of the third line in each stanza. Something similar happens in “The Birth of Language,” (read it here) where Lewis uses an ABCB DEFE rhyme pattern, but rhymes the first half of the first line with the second half of the line, and the first half of the third line with the second half of the third line (in each stanza).
Or take Lewis’ poem, “Le Roi S’Amuse” (read it here). Its rhyme pattern for each stanza is AABCCBDD. The two “B” lines, furthermore, each have internal rhymes, where beginning and end match. And perhaps even more important than the rhyme scheme is the syllabic patterning. The first line of each stanza is two syllables (except in the final stanza). The second line is five syllables. The third line is ten syllables in most stanzas. The fourth line is four syllables (give or take). The fifth line is five syllables (or, rather, the rhyme is at the fifth syllable; except in one stanza where the rhyme is at syllable three). The sixth line is 11 syllables (give or take). The seventh line is 10 syllables (give or take). And the eighth line is twenty syllables (give or take).