If you are looking to book your next flight within Europe than they are offering you a £20 discount on economy short-haul destinations. https://promotion.lufthansa.com/amexoffer20/
If you are looking for something further afield then they have £50 discount on economy long-haul destinations.*
* Offer is not valid for trips to the USA.https://promotion.lufthansa.com/amexoffer50/
Offer valid for bookings between 1 April and 15 May 2010 with outbound travel commencing on or before 31 August 2010.