The process is a bit strange because we'll be installing an icon set we won't use and swapping it for one we want -- a bait-and-switch, I suppose.
Install Crystal Theme
First, let's install our 'place-holder' by pasting the following into the terminal.
sudo apt-get install libreoffice-style-crystal
Download and Faenza Theme
You may download the theme from gnome-look or a quicker download:
Make the swap.
First get root access to modify the themes.
gksudo pantheon-files /usr/share/libreoffice/share/config
Remove or change the name of images_crystal.zip. I changed it to images_crystal_old.zip for safe keeping. Now swap in your newly downloaded file into this same directory. Your folder should now look like this.
Make it official!
In LibreOffice, navigate to Tools → Options → LibreOffice → View and change the icon theme to Crystal.
Enjoy!