Best (cheapest) way from Lubeck to Hamburg?
Is there any group ticket?
Any commuter trains?
If you take the Regional Express trains via Bad Oldesoe, you can buy a "Kleingruppenkarte" for up to 5 people for EUR 34.50. The ticket is valid after 9AM on weekdays, all day on weekends and holidays. Fare is available on the Deutsche Bahn's website en English, as well as on the NAH website in German only.