You could e,ail yourself the you could email yourself the lyrics and then copy them from the email into the notes app. The app option I would prefer but here's another option if you want
You can save the lyrics in PDF format using Microsoft word, email them to yourself and open in iBooks on your iPad and it'll stay in your iBooks for quick access? If you have pages app it would be even easier to store the lyrics there
I'd probably create PDFs of the songs first. At that point there are a number of apps that would work well, but I would probably use iBooks because I like the interface.
I'm a musician as well and have found the PDF reader built in to iBooks to be very good. I do a lot of arrangements throughout the year for area schools (usually high school musicals--putting songs in different keys and stuff like that.) The directors usually e mail me the originals in PDF format and I save them in iBooks. I can then put my iPad on a music stand and have it right next to my PC where I'm inputting notes. It's crystal clear and I can't accidentally put any pages out of order. I love it.