Lufthansa has been rolling out their satellite based WiFi throughout their fleet. It's now available on most long-haul aircraft. I posted a review for their version of Internet back in May. It's usually a good product – not good enough to do a lot of muti-media or heavy browsing but good to read Facebook and your emails.
Lufthansa used to charge for Internet irrespective of the cabin (one hour EUR 9.95). However during my two First Class segments over the weekend it was free. I'm not sure it was because of my existing cooking from the Lufthansa lounge or because Lufthansa is temporarily not charging.
However you can't connect an iPhone with iOS 7 since the page where you accept the Terms & Conditions can not be clicked on a phone. It's easy enough to use on a laptop though.
Amazingly enough the service is available almost everywhere Lufthansa flies with the exception of China.