Add Lyrics to iTunes with a program I've been looking for a program ,or a widget, that could search for lyrics, download them and add them to iTunes (or display the lyrics while I'm playing a song).

All those I could find were outdated and didn't work correctly.

There are other program that can search for the lyrics but do not add them to iTunes, others that display lyrics already in iTunes but not both.

iTunes version : 12.3.0.44

OS X version : Yosemite (10.10.5)
You should try jwzlyrics. It picks up songs changes in iTunes (and Spotify), finds lyrics and displays them in a window.

It's dependent on https://lyrics.wikia.com/ for it's lyrics, and works quite well for me.