Delta has announced that, like Lufthansa, it would have to start paying for the new European carbon-exchange tax. Unlike Lufthansa's earlier confused announcement, however, Delta said straight out that it would add a "surcharge" of $3 each way to tickets to/from Europe.
How will you see that surcharge when you buy a ticket? Delta hasn't responded to my follow-up question yet, but when I entered its booking process, the surcharge was apparently lumped in with a handful of other "international" taxes and fees and not shown separately. For now, Delta continues to adhere to the old U.S. rules on fare advertising (under which it's acceptable to omit some taxes and fees from the initial fare display), but it will presumably go to all-up displays when the new U.S. rules go into effect later this month. We'll see.
Regardless of how they present the charge, Lufthansa and other airlines will probably add about the same $3 to compensate for the new charge.