Lyricfier is a program that lets you view the lyrics of the songs playing in the Spotify desktop client; the lyrics are displayed in a pop-up window while you listen to the music.
The pop-up window can be moved and placed anywhere on your desktop, so you can always have the song's lyrics in view.
Once you download the program from its official page, you'll see the pop-up appear on your desktop, and when Spotify changes songs, the window automatically updates with the new lyrics. You can't save the lyrics to your computer, but you can copy them and paste them into a text document.
How to Use Lyricfier
It's very simple: first, open and play a song in Spotify, then run Lyricfier, and you'll automatically see the pop-up window display the lyrics for the track that's playing.
It's truly a great option for reading the lyrics of songs playing on Spotify. Everything happens automatically, and you don't need to configure anything at all. Generally, it shows the lyrics in the original language of the song, although it detects the operating system language and, if the lyrics are in Spanish, it will show them.
Lyricfier is a free, portable Spotify client available for Windows and Linux.