For us, it's Bible readings left-justified, song and hymn lyrics centered. Left-justified blocks of text are easier to read*...but songs aren't blocks of text. They are more like poetry, which doesn't have any hard-and-fast rules about alignment. And unless you have lines with drastically different lengths (which given the nature of musical phrases, doesn't happen enough to be a big problem), lines are generally of similar enough length that centered vs. left-justified doesn't make a big difference in terms of readability.
(* There are a number of things that impact readability of text, not the least of which is the font selection. The "rule" about serifs and readability doesn't really apply to on-screen text, it's more for blocks of printed text. Another thing that impacts readability is line length. Lines that are too long or too short are harder to read, too. But "too short" doesn't apply to songs unless you're breaking up a phrase.)