The old city of Lübeck with its medieval 5 churches and their famous 7 towers, the Holstentor and lots of nice buildings and streets is worth a long walk. You should also take the time to explore the surrounding parks ('wallanlagen'). You have scenic views on the town but also a good number of birds, some of them are easier to see in these habitats than in pure nature, such as Goosander, Peregrine Falcon, Eurasian Treecreeper, Black Redstart or Eurasian Jackdaw. In breeding season you can also observe Lesser Black-backed Gull easily, which are rather rare in the east of Germany and inland. Some roofs hold breeding Eurasian Oystercatcher and the river Wakenitz is worth a swim and also good for Common Kingfisher or Grey Heron.
Parking and driving is difficult in the city as one tries to get out as many cars as possible. You should park around the city or just take a bus and walk.