Usually an International driver license is available for 3 years for stays of less than 3 months perhaps it is different depending on the country - check your IDL - in any case you will not have a problem with the police but perhaps in the event of accident with your insurance
I never had problem with Lufthansa flying with a one way ticket 99,99% of the time no one check this the best thing is to do a self check-in with only cabin luggage