Use of any cellphone, text messaging device or portable music player while on the scooter is also against the rules.
There is also a maximum weight limit of 136kg.
And insurer IAG which owns State Insurance, AMI, NZI and Lumley says anyone using the e-scooters who doesn't stick to the agreement may not be covered under an insurance claim.
Safety concerns about the scooters have been raised by Auckland Council and since their launch for public use nine days ago 14 riders have lodged ACC claims for injuries.
Lime's user agreement makes it clear that any liability for accidents rests entirely with the user and states that anyone who has an accident which involves personal injury, property damage or the scooter being stolen must report it to the local police department within 24 hours.
But Sasha Cowlrick, executive manager consumer insurance at insurer Vero, says while new app-based services like Onzo bikes and Lime are great for giving Kiwis new clean transport options they leave an insurance liability gap.
"They do leave an insurance gap that many of their users may not be aware of – liability cover if anything goes wrong."
Cowlrick said in New Zealand anyone using a bike or a scooter (or their e-versions) could be liable under various laws if they injure another person or damage someone else's property.
A person who owns their own bike or scooter can insure against the cost of a potential accident through taking out contents insurance.
But covering rentals may be up to the individual insurer.
Cowlrick said Vero's contents policy would cover rented e-scooters and bikes but urged people to check with their insurer if they were covered.
The Herald contacted major insurers AA Insurance, Tower and IAG who all said e-scooter and bike rentals would potentially be covered under contents insurance.
But IAG, which is the largest general insurer in New Zealand, warned people may only be covered if they meet the terms and conditions of the company providing the service.
Chris Kiddey, IAG New Zealand's national technical special said: "In general, IAG contents policies may provide liability cover, provided that the user meets Lime's terms and conditions and is taking reasonable care to avoid a loss happening."
Kiddey said it recommended e-scooter users read the Lime terms & conditions before use so they know what their responsibilities are.
"We would strongly encourage users to follow the road code and take heed of any rules, such as age restrictions, use on the road rather than footpaths (same as a pushbike), and use of helmets."