How do I obtain the free Adobe Livecycle Designer upgrade? I have a user that we upgraded from Adobe Acrobat X Pro to XI Pro and he really misses this add-on. I understand that if I contact Adobe I can obtain this download.

First step is to build a time-machine and then go back about 5 years in the past...

Seriously, though, you're way too late. Acrobat XI isn't even the current version anymore. It was superseded by Acrobat DC and that offer has long since expired. If you want LCD you'll need to purchase it now as a standalone application.