The lawsuit comes after Lime released more than 1000 e-scooters into New Zealand last week.
Six-hundred of them were released into Auckland but complaints have surfaced already around some users riding them dangerously around the city.
Two safety campaigners have claimed, separately, that deaths are inevitable if their recommended changes are not implemented.
One Twitter user wrote: "I nearly got knocked over by one in the viaduct."
A commuter told the Herald that Auckland Transport staff were seen on Monday running around the viaduct trying to get people off the scooters.
A spokesperson for Auckland Transport said they had worked closely with Auckland Council on Lime's licensing and welcomed its service, but would be monitoring the situation.
"We will continue to monitor the services and make sure the numbers of scooters and shared bikes introduced is appropriate for the city centre and surrounding areas," a spokesperson said.
Another Twitter user wrote: "There were a couple of scooters parked in the middle of the footpath on Queen St, causing trip hazards to pedestrians on foot. Do contractors pick these up too? Love the concept but will there be designated parking zones in the future or is it a parking free for all?"
According to the Auckland Council, one person has so far complained to them about a scooter that was parked dangerously.
In a statement to the Herald, Auckland Transport said it was up to users to leave them in an appropriate public place.
"Lime's licences, granted by Auckland Council, set out the locations that the service provider can leave them, and users are encouraged to leave them in appropriate public places and make sure there is space for people walking," a spokesperson said.