It's been awhile, but I think I installed it using good ol apt-get.
sudo apt-get install attract1
That installed version 2.2 which, looking at the Attract Mode homepage, isn't the latest version (2.3 is). But the .deb available on the site is 2.2 also, so maybe 2.3 isn't available for Linux yet.
Anyway, version 2.2 is working beautifully on both Lubuntu machines I have it installed on.
One thing to note is that it installs to a hidden folder for some reason (~/.attract).
Feel free to post if you have any issues or questions.