To some extent SongMaster Pro can do it.

Just drop the file into SMP and it will analyze the song for the chord structure.
You can have it play from from the tracks (mixer), chord table or the Song Sheet View (similar to what is asked for above) Song Sheet View

It rolls ie follows the song as it plays no need to change the pages.

It can search and download Lyrics from the web.

Importing Lyrics
...... "Lyrics come in two flavors: synchronized and unsynchronized. Synchronized lyrics have a timestamp associated with each line of the lyric that is used to match it to the time the lyric is sung in the song. Unsynchronized lyrics are just the text (they don't have a timestamp). Song Master works with both types, however, of the two, synchronized lyric format is preferred"....

It seems to work smoothly as long as it can find synchronized tabs for the song otherwise one need to manually line up the lyrics or if not found at all manually enter the lyrics and line it up.

They have trail versions just do download and check it out.
SongMaster Pro