Rather than searching online for other other people's versions of songs, this app displays your lyrics, which you've formatted as you want them on your computer. You can create them in Pages 09, Doc, pdf, rtf or txt format [Unfortunately Apple don't yet allow apps to use the new Pages 5 format - this should be resolved in a future iOS update] then simply transfer them to your phone using the iTunes file transfer system (on the Apps tab for your device). While primarily designed for singers, the new improved pdf handling makes PDF scores look amazing, so the whole band can get in on the act.
Not only does My Lyric Book remember your lyrics and set lists, but songs can be tagged with a tempo for the built in metronome, or linked to tracks in your iTunes library so you can refer to a recorded version or play a backing track from within the app. You can even send midi patch changes, so selecting a song programs your keyboard for you!
If the rest the band is using the app too, then you can all sync up, so that the band leader can select songs and have them automatically selected on everyones screens. (Note this DOES NOT distribute the lyrics, but selects each band member's version, so each band member can see their own parts as they've set up their devices).
Of course your lyrics look even better on an iPad, but an iPhone or iPod has plenty of screen space to display lyrics and you can always have it in your pocket.