you can always jump into your precomp and edit your animation there.
If you need another copy of the same precomp, just go in the Project panel, duplicate it and drag it into your timeline where you need it. This second precomp is now independent from the first one.
You might find useful to have an audio reference track for your animation in your precomps too.
I have probably done 250 to 300 "lyric videos" or more accurately dynamic text animations. Here's what works best and is fastest in the long run.
Break up the script into sentences or short phrases. If you know how to analyze the audio track using premier/audition and drop in markers for each word to the audio file. (This is and advanced technique and you can find a tutorial on Adobe TV)
The next step is to create a separate comp for each phrase or sentence then render those comps and do the final edit in a nonlinear editor like Premiere Pro.
Another trick to help speed up production is to start by playing out your type for each key phrase in its hero position first and then working backwards and forwards from the middle of the timeline to create the animate in and animate out for that phrase.
Trying to do a three or four minute "lyric video" in a single composition will take you three or four times as long as it would to break things up as suggested. Three or four times longer is a conservative estimate for someone experienced in creating animations with AE.
More info on the much missed speech analysis can be found here: Using Speech analysis in Premiere Pro CC