If you want create short lyric video, for example musical video with lyrics scrolling, I suggest you to try Lyric Video Creator software.
It is a windows software designed to synchronize lyrics with the mp3 song and save the result to MP4 Video format (compatible with Vevo too)
As backgound is possible to set a static image or a video.
From Options it is also possible to choose video resolution (480p is recommended), lyric font type and size, scrolling mode, etc.
This is a screenshot of the program:
There are good numbers of programs that can be used as a video production for motion graphics. So if you want to become a Lyric Video Maker, check out these applications.
Adobe After Effects
Premiere
Sony Vegas
even iMovie or Movie Maker.
You can also find a great number of tutorials online on how to use these apps.
However, if you are an artist looking for a professional lyric video company, you can hire some of the best in the industry 351 Studio. Lyric Video Maker.