The music app I developed called "Music Player (Remix)" supports reading lyrics embedded in the music files (within the tags). It also downloads lyrics for songs with no embedded lyrics and stores the lyrics within the music files (there's also an option to store the lyrics in a separate text file). And as an additional bonus, you can record yourself singing along while viewing the lyrics (what I call "karaoke mode").
You can find the app here in the Play Store: https://play.google.com/store/apps/details?id=com.hedami.musicplayerremix
Free 14-day, fully-functional trial version can be found here: https://play.google.com/store/apps/details?id=com.hedami.mprtrial