If you get this before you go you need to cross the airport car park to the main road and the bus stop is on the main road - do not cross the main road though. Stay on the bus as it goes through the town and look for Macdonalds on the right hand side after passing this get up and ring the bell and I think you should be at your stop. If all else fails the bus station is only just past the gate and you can walk back which is not very far. The train station is behind the bus station and ask at the information desk and they will tell you the cheapest ticket to buy to go to Hamburg - cheaper than the ticket machines and they do speak English. Lubeck isn't enormous - we went in December last year for the Xmas markets and the Ice show but plenty of shops for a look round and a few historic sites. Some nice restaurants by the river just up from the gate.
Hope this helps and have a nice time

Isn't Lubeck famous for its Marzipan?

Just back today. Had a good time. Didn't read that reply before I went, but I knew about the bus anyway. Thanks though, good directions!

Bus is 2.05 euros if anyone is interested. Really quite liked it, although we only had a flying visit I think we packed plenty in. We had lunch at Subway (I know! but it was just what we wanted), and then had dinner down near C&A in an italian restuarant with outside seating and heaters.

Went to several churches, the Dom and the shops. Went to Jazz cafe in the evening, and then onto Finnegans Irish bar.

Would recommend it for a short break. I did notice that compared to Cologne they didn't speak English just as well. So I got to try out my German!