Integrating GetResponse autoresponder with Joomla CMS will definitively be trickier than integrating AWeber because it seems there's way less material covering GetResponse integration in general, including on their own site and support forums. There is no API or database integration. There are settings where you can email to a specific email (e.g. subscribeme@yoursite.com) and get added though which could probably be leveraged to achieve this.

Ideally, when a new member subscribe to your Joomla site, he would then be subscribed to one of your lists (or at least a confirmation email from GetResponse should be sent to his email address) and then later on he would have the choice of subscribing to more lists directly from your Joomla site.

Well, it's definitively not that simple, here's what I've found: