first of all

it's badly written. start a new sentence at the second Hamburg.

I interpret the meaning of this sentence as: Hamburg's importance as an economic city grew thanks to its port as well as the foundation of the Hanseatic League.

Then Hamburg's importance as a hub of commerce began to grow when the Hanseatic League was founded in Lübeck and Hamburg provided the port facilities that opened the way to the rest of the world.
It would be best to have the original German sentence. Not sure about the last part.

Here are some of the problems and some suggested solutions:

1. "Hamburg’s importance as an economic city THEN grew":

"Then" probably refers to a time frame that is implied in the context. Here it probably means "from that point on."

2. ". . . AS the DEVELOPMENT of the Hanseatic League was founded in Lobeck":

The word "as" here serves both as a time reference and as an explanatory device. The rise of Hamburg was concomitant with the development of the Hanseatic League in Lobeck. This part of the sentence is particularly unelegant because it is overdone. The word "development" is superfluous. One should either speak of the development of the League or its being founded, but not both, at least not in this manner.

3. ". . . AND Hamburg provided the port facilities":

The coupling of this part with the preceding part is also unelegant. The writer wants to expose the connection between what was going on in Lobeck and the role of Hamburg in that development, but the use of AND does not really help. A full stop and a fresh start would make for a less monstrous sentence and a better flow of ideas.

4. ". . . WHICH opened up the way for the rest of the world": This is another instance of ineffective splicing of clauses. The word "which" is ambiguous. It is not clear what exactly opened up the way for the rest of the world. Was it the ports?

Here is how I would tentatively re-write it:

Hamburg’s importance as an economic city grew from that point on, as the Hanseatic League was founded in Lobeck. Hamburg provided the port facilities for the League, and [something not quite clear from the sentence] opened up the way for the rest of the world.


Fuad

...not because he maintains a single sentence (I don't think it matters if you put it into one or two sentences), but because his phrasing maintains the relative importance of the port facilities to Hamburg's economic importance.

I think the answer you chose is okay, but I don't quite get the same sense that the port facilities were equal to the Hanseatic League to that development in Hamburg.

Either one is satisfactory, however.

"Hamburg’s importance as an economic city then grew as the development of the Hanseatic League was founded in Lobeck, and Hamburg provided the port facilities, which opened up the way for the rest of the world."

"as" could be read to mean "because...X was founded" or "at the same time as ...X was founded". Ambiguous maybe, but not wrong per se.