The answer lies in the geographic and political situation of the Baltic Sea.
First, geography is a major factor: Take a Mercator map and loop at Europe: you'll ask your question. Now take a terrestrial globe. You'll notice that the Mediterranean Sea is bigger than the Baltic Sea. It has more and bigger islands. Now, add to this fact the fact that all the North of Baltic Sea, stuck between today's Sweden and Finland, could not be successfully used during the Midle Age. By that time, the Northern extremity of Europe was the island of Gotland.
In today's Germany, land was not "free" as in Balkans for Venice, it was already occupied and under the Holy Roman Empire, that would not be in favour of war between its cities: if Lubeck had attacked, everyone would have coalized against Lubeck.
So overall, there was no room for colonies nor territories.
Second factor, the political situation saw the Hanseatic League: a league of cities such as Lubeck that organized themselves for trade with other cities or countries. They used their commercial power and treaties to ensure advantages for their merchants in foreing cities, creating multiple commercial posts similar to Venitian ones in Egypt, Constantinople or the Holy Land. Again, territories in England, France or Dutch were occupied and Lubeck had no room for colonies.
This idea of "room for" is not only about military strength, but also about political situation: it was easier for Venice to conquer Muslim or Byzantine held territories than for Lubeck to fight other Christian territories.
Then of course Lubeck could have "tried" and sail to Greenland, that Vikings had talked about, or even America. But this was far more risky than going to Creete or Cypress for Venice.