Yup. You do the karaoke version of Bach's Mass In B Minor and you're talkin' a whole boatload of layers.
This is about a zillion times easier and faster to do in Premiere Pro with simple animated titles. It's far easier to do longer projects like this in a NLE.
If you insist on doing everything in After Effects then you're going to end up with a separate layer for each line of lyrics that you want to animate across the screen. There are ways to analyze a voice over track in Premiere Pro and extract the words, then put those words on markers in an audio file and import that file into AE to help you with the timing, but it's still going to be easier in Premere Pro.
Here's what I would do. Watch this tutorial on creating a Live Text Template in After Effects to use in Premiere Pro. How to use Live Text templates from After Effects in Premiere Pro | Adobe Premiere Pro CC tutorials
Back in AE build a template long enough for your longest phrase and set some place holder type
Open the Advanced tab in the Composition Settings and check the box that says Editable In Premiere Pro
Save the AE project and import it into Premiere Pro
As you drop each new phrase into Premiere Pro adjust the timing of the words buy using the time stretch tool in the Sequence Timeline
That's about it.
If you want three or four styles of fade in and out then make 3 or 4 template comps.
If you stay inside AE just start adding text layers, text animators and key framing all of the words by hand. Creating some animation presets may help but the first suggestion will be the quickest.