One possible plot could be that Bilbo, being blind, has to rely on the kindness of the Laketown people to survive his sickness. Maybe he befriends a local healer who tries different remedies. The people of Laketown might initially be suspicious but then grow to care for him as they learn of his adventures.
In a 'blind bilbo sick in laketown' fanfic, the story could start with Bilbo arriving in Laketown already in a weakened state due to his blindness and sickness. He might be found by a family who takes him in. As he recovers, he could start to tell the children of the family about his adventures in the Shire and his encounters with dwarves and trolls. This could inspire the children to be more adventurous themselves. Meanwhile, the adults in Laketown could be dealing with their own problems, such as shortages of food or threats from outside forces, and Bilbo's presence could bring a new perspective to their situation.
Well, perhaps Bilbo's blindness and sickness are the result of some dark magic he encountered on his journey before reaching Laketown. In the fanfic, the people of Laketown could be divided in their opinions on helping him. Some might think he brings bad luck, while others see him as a heroic figure in need. His struggle to regain his health while blind could involve him using his other senses more acutely, like his sense of smell to detect if a medicine is good or bad.