Falzone said Lime's app includes language that specifically instructs people not to operate scooters on local footpaths, pushing them onto city streets instead.
Operating a motorised scooter on the street is against the law in Florida and in Fort Lauderdale, though the city does permit e-scooters to be ridden on footpaths.
Because she followed Lime's instructions, Falzone said, Jordan avoided the footpath and was catastrophically injured.
"To this day they are telling users to break the law and, as a result, people are doing that," Falzone said. "They are getting hit by cars, they are hitting pedestrians, they're having all manner of accidents that shouldn't be occurring."
"Unfortunately," he added, "Ashanti is going to pay for this with her life."
Lime did not immediately respond to a request for comment.
The lawsuit arrives about a week after a 21-year-old exchange student from Ireland was killed in an accident involving a Lime scooter and vehicle in Austin, Texas. The student, Mark Sands, appears to be the third person killed in an accident involving Lime scooters in recent months.
The Centres for Disease Control and Prevention is studying the health risks associated with e-scooters by analysing injuries to riders and pedestrians in Austin, Texas, over two months. Last week, a CDC spokesperson said that the study should be finalised in the northern spring.
In Fort Lauderdale, Florida, where e-scooters arrived in November, a series of high-profile accidents has raised controversy over the devices, according to the South Florida Sun Sentinel.
"According to Fort Lauderdale Fire Rescue, between December 1 and January 31, there have been 40 incidents involving scooters," ABC affiliate WPLG reported. "A total of 31 of them required someone be transported to the hospital, and four of those were level-1 traumas."
Lime, which has admitted that some of their models have caught fire and broken in half while being ridden, has received hefty investments from Uber and Alphabet and, according to Bloomberg, is valued at more than US$1 billion.