The Rhythmbox version that was first hosted on sourceforge (v0.8.5) first existed with a GUI as per your second screenshot.
Since the software was moved under the Gnome umbrella, the GUI has been changed as per your first screenshot. Unfortunately, you cannot reskin rhythmbox to have the old GUI.
There is a rhythmbox fork:
The second screenshot looks very much like the proposed "Rhythm-e" elementary version of Rhythmbox - this is/was a fork of Rhythmbox proposed for Elementary OS.
The current status of Rhythm-e looks rather quiet looking at launchpad
The screenshot is from a webupd8 article
There are some nice screenshots of this on deviantart - Rhythm-e is deprecated and is no longer being developed, Beatbox which is the new Music Player from the elementary team was favored over Rhythm-e. However this is not available in Lucid.