Usually, the best way to explore any city is on foot. Lübeck is certainly no exception to the rule. The city has a rich history and parts are not accessible by car at all.
The tourist agency for Lübeck lists two city walks on their website (http://www.luebeck-tourism.de/, go to Info Lübeck, then click Sights) that will take you past several of the highlights.
Lübeck is most famous for its seven church towers that characterize the skyline since the Middle Ages. But the city defense works and the city hall are also sights not to be missed.