LiveCycle is bigger than life! I cannot alone do justice to the question but I shall do my bit :-)
From a perspective of convincing management you can share the success stories of dozens of organization shared at http://www.adobe.com/cfusion/showcase/index.cfm?event=finder&loc=en_us&productid=256886. Also, have a look at this What is Adobe LiveCycle blog post. Hope these few pieces of the jigsaw get you closer to the answer you seek.
And also Tour de LiveCycle was created as an 'introduction to Adobe LiveCycle' among other things. The content may be slightly dated but you should be able to find some great introductory material in there. Access it from http://www.adobe.com/devnet/livecycle/tourdelivecycle.html and see if it serves your purpose.