In ordinary narrative writing, sentence fragments are no-nos. In lyrics we use them all the time. Often lyrics wind up clunky and less rhythmically assured if we assume we need to write in complete sentences.
You can get some practice with lyric “raw material” in sentence fragment form by using sense-based writing tools, like the object writing techniques Pat Pattison has introduced in his books. These involve generating associative streams of words, not yet intended as rhythmically or rhymically shaped lyrics. (Wait—is “rhymically” a word? “Rhymic” apparently is, so why not?) When writers first try such techniques, their prose is often too “journalistic” and correct, as if they were constructing polished short stories or essays. This generally means words are not flowing out fast and loose enough: there’s too much editing going on. To defeat this, some writers try spitting out isolated words in lists. If you’re object writing about an apple, you’ll get: “Red. Sweet. Crunchy.” The sweet spot for the best object writing “flow” is between these extremes: the phrase or sentence fragment is perfect. A series of sentence fragments creates snapshot pictures or other sensory “bursts” for the reader, and potentially for the listener as well. And, while the goal of these techniques is not to arrive directly at extended lyric passages or entire lyric sections, it is possible to lift out isolated gems—an image, metaphor, phrase or line—into song lyrics. These will often take the form of sentence fragments.