You also receive a companion pass after the first use and upon each anniversary; the companion pass is good for coach class on Lufthansa flights from U.S. to Europe/Africa/Middle East/Far East on H fare or above (H fare is between the most discounted fare and full fare) and you still have to pay the taxes and fees for the companion (the fuel surcharge can be pretty high); the details of the companion pass can be found here.
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