Peter, I often send the lyrics to a second display/projector for other band members. I use either a lightning to hdmi or a lightning to vga adaptor and just mirror the screen. It also does work well to an Apple TV box but then of course you need a common network to connect to so maybe good in a fixed setting like a church but a pain at a travelling gig.
to get the best lyric only display its best to use a 2nd iPad using the stage traxx network facility. Especially as you can now tailor the lyrics on the 2nd pad and you don’t need a video lead from the original source ipad