After trading along the frontier and likely in Detroit, La Lime arrived in the Chicago area on August 17, 1792 as an agent for William Burnett of Canada. In 1800, he purchased the homestead of Jean Baptiste Point du Sable for Burnett for 6,000 livres. The bill of sale was filed in Detroit, Michigan on September 18, 1800, although dated in Chicago on May 7 of that year.
By 1804, Burnett's partner, John Kinzie, who also settled in Chicago, had bought the former du Sable house. He lived there with his wife and first child. They had three other children born in Chicago.
After the Americans established Fort Dearborn in 1804, La Lime worked there as an interpreter, aiding communication between the Americans and Indians. He broke his leg in 1809 and, as it was improperly set, was left lame.
On June 17, 1812 in Chicago, La Lime and Kinzie quarreled, and Kinzie killed him. Kinzie fled to Milwaukee, then in Indian territory. He claimed La Lime had shot at him and he had stabbed the interpreter in self-defense. Historians have speculated that La Lime was acting as an informant on the corrupt economic activities within the fort, and Kinzie killed him to silence him. It has been also proposed the Kinzie's attempted to cover up the families early real estate transactions, substituting Francis May as the original owner (who died after eating at the son's [James] home).
La Lime was originally buried within sight of Kinzie's house, as the European settlement was thinly strung along Lake Michigan. Kinzie maintained the gravesite. After he died in 1828, his son John H. Kinzie had La Lime's remains exhumed and reinterred in the churchyard of St. James Church.
In 1891, a coffin was discovered at Wabash Avenue and Illinois Street near the Rush Street Bridge. Based on the research of Joseph Kirkland, the bones inside were believed to be La Lime's. The remains are held by the Chicago History Museum.