Lübeck, Bremen, and Hamburg were three of a surprisingly large group--around 50 or so--of what are called "imperial free cities." These are by no means democracies, republics, or independent. They were part of the Holy Roman Empire, and representatives from the imperial free cities for a time constituted one body of the Reichstag.

What distinguished these cities and towns from others was a legal status called Reichsunmittelbarkeit, or imperial immediacy. They were not subject to their territorial lord (the duke of Bavaria, the duke of Saxony, the archbishop of Cologne...well, that one was contentious) in the sense of taxes, laws, religion (after the Reformation) or supplying troops. They answered instead directly to the emperor--hence, imperial immediacy; no intermediary.

Different cities had slightly different governning structures, but these were by no means democracies. First, of course, women had no place in government. Second, in the case of cities whose legal jurisdiction encompassed its hinterlands--Nuremberg is the most prominent here--people outside the city limits but within the legal limits had no citizenship rights.

To get a bit more complex, the social structure in most of these cities, at least the southern ones that I'm more familiar with, included a group of designated "patrician" families (kind of a proxy for nobility) and then regular burgher families. Patricians, a smaller and more prestigious group if not always wealthier, generally had most of the seats on the town council reserved for them. In Nuremberg, most of the special responsibilities of the council were reserved for the ~80% of members who were patricians.

This inner council wasn't elected by the people at large, though. There was a second, larger council, made up of a few hundred representatives of the city's wealthy burghers and patricians--basically, successful business owners and merchants, not day labourers or those working in unskilled trades. Their typical responsibility was to rubber-stamp the decisions of the small council. In elections, however, the larger council would select representatives of the small council to choose the next small council. Unless a councilor seriously messed up, they typically served for life or until they chose to step down.

The imperial free cities weren't geographically bound to a particular principality. The southern ones and Strasbourg have been studied in great detail thanks to their significance in leading the Reformation (often against the will of the duke in whose territory they lay, e.g. Bavaria). There were a lot of ways a city could gain imperial immediacy. The easiest was to start out with it, of course. However, getting really rich and successful in trade could help in a couple ways. First, although it made the city an attractive thing to "possess," if a prince fell onto hard times, a richer city could buy its free status. Lübeck, which gained Reichsunmittelbarkeit in the 13th century, was powerful enough to negotiate similar status for other Hansa cities and towns. So there might have been some factors in play that led a group of northern cities towards imperial immediacy, but it's nothing nearly so straightforward as a link between democracy and the power of merchants with money.

Also do the republics from this period have any established connection to the ancient Germanic "Things" (tribal assemblys) attested by Roman sources?