To expand a bit on my previous response...
If you simply want to display the lyrics of a song, while that song is playing, you can copy the lyrics from the lrc file and paste them into the lyrics page of the song in iTunes. As you have noted, the lyrics will display as one page (that you manually scroll) on an iPod, iPad or iPhone. You might want to check that the lyrics are correct.
If you want the lyrics to display only when that line is due to be sung, together with the moving dot to indicate the timing of the singing, you will need the karaoke version of each song (usually without the vocals) and a karaoke machine to instal that song and the lrc file onto. Special codes in the karaoke version of the song will prompt the machine to display the appropriate line of the lrc file, as-and-when required.
iTunes does not have the necessary software to control the lrc file.