While the fishermen know the waters well, it's not entirely unknown for one of them to go missing. Sometimes this may be because of an unexpected storm, or due to human error or some other relatively natural cause, but sometimes something else is responsible. There are things in the ocean other than fish.
Example: An old fisherman named Jakyb Wyzor didn't come back last night, and his family is begging for someone to go looking for him. They know where he was planning on fishing that day, and if the PCs go there they find a strange portal in the waters, perhaps a relic of some wizard's experiment. Do they dare go through the portal to see where it leads?
The smuggling trade carried out in Fishertown is something that PCs could potentially get involved with—either trying to stop something from being smuggled in or out of Lüm, or, for less scrupulous PCs, trying to smuggle something in or out of the city themselves.
Example: A priceless statuette has been stolen from a museum in the Arts District. The museum staff would rather not involve the guards if they don't have to, because the item was on loan from a wealthy benefactor and they don't want word of its theft to get back to her, so they're making excuses for why it's not on display—but they're willing to pay well if someone else will look into the matter. The curator is pretty sure the thieves plan to smuggle the statuette out through Fishertown; can the PCs find them and retrieve the item before word spreads that it's missing?
The fact that historicartifacts occasionally turn up in Fishertown is another thing that might end up involving the PCs. The PCs might be interested in searching for such artifacts themselve, or they might get in the middle of a fight over such an artifact—or have to deal with the fallout of the discovery of an artifact with dangerous magicalpowers.
Example: A universityarchæologist hears that a young oysterman in Fishertown has accidentally dredged up an ancient magical bracelet from the early days of Lüm, while it was still an independent city-state. The PCs go to investigate, but find that the bracelet's discoverer has learned it has potent magical abilities, and isn't willing to part with it at any price—worse, he plans to use it to extort the people of Fishertown and put himself in control, and later expand his dominion to other parts of the city if he isn't stopped.
As mentioned in the goods and services writeup, one reason the PCs might want to go to Fishertown is to hire a boat from the local fishermen. For any adventurers involving traveling in the waters outside Lüm, Fishertown is a natural stop.
Example: A strange creature has been sighted in a certain part of the waters outside the city, perhaps the result of a summoning gone wrong, and there are worries it might be a potential danger to the city. The PCs are tasked to investigate, but none of the ships at the main port want to go near the thing. Can the PCs perhaps persuade a resident of Fishertown to loan them their boat, or perhaps to row them out there themselves?