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You can become a member of the Miles and More program and apply for any travel rewards credit card issued by a major bank to earn and redeem rewards with any airline. For example, there is the Discover it® Miles card that will allow you to earn miles on all your purchases. Earned miles can be redeemed with Lufthansa and any other airline. Another good thing about this credit card is that it does not have an annual fee. Most airline credit cards will charge you an annual fee.