LH also offers in First but using a voucher.
Out of my four recent F flights, on three the voucher worked very easily, and on one of them there was a problem by which none of the vouchers onboard were working, but buying unlimited access for about EUR19 on the 12 hour flight was possible. Crew were very apologetic, and offered that since I could not use the normal internet voucher, they offered me EUR25 service recovery voucher to use in their shopping on that or any future flight. I bought the internet access on my credit card, used the voucher to by a gift on a future flight, and felt they had done right by me on the flight where a glitch prevented the usual service from working.
As others have noted, TK gives this to elite card holders in all classes, as well as to business class passengers, which is the way I think any serious airline should be looking at the equation. So often, the time and resources spent executing the payment process for these passengers is really just a thorn after either the cost of a F/J ticket, or a complete waste of time for the passengers who are taking enough flights to hold higher status. When we're already at the point where this service can be sold for EUR19 on a 12 hour flight, once has to wonder if it's not simply better and even transactionally equivalent for the airline just to comp the service in the same way as extra baggage or free seat selection, both of which are already much more expensive than internet.