Air carrier Flight Attendant reported the flight attendant manual had no information regarding the cabin storage of a mobility lithium ion powered device. Ultimately the Captain approved the cabin transport of the device.

Narrative

20 mins prior to door closure; handicapped passenger rings the call button and tells they never received a tag for their walker; so I let the agent know and she says she's working on it. The walker was placed on the opposite wall so I stepped off the aircraft to ensure I could keep an eye on it. The agent comes down and tags it while I'm making announcements and closing bins; I come up to the front of the cabin; I no longer see the walker and I ask the agent if she gave the tag to [the passenger]. And she proceeds to call a ramp agent; and lets me know there's another problem regarding an electric scooter and the ramp agent needs to speak to the Captain?!? I ask the Captain to come outside and let him know there's an issue regarding an electric scooter in cargo and I also ask if he can retrieve the tag for the walker. The First [Officer] says he'll take care of it on landing and the ramp agent proceeds to discuss with the Captain regarding the scooter's battery (lithium or wet/dry cell). I make final boarding announcements. Passengers are getting worried about their connections so I ask the captain to make an announcement. Captain asks me if I can store a lithium battery in the cabin. The Captain requested to see the scooter while I searched in my manual; I found no place in the manual regarding scooters. But I did know that it could not be stored in cargo; I ended up placing it in the overhead bin with the Captains permission...after ensuring it was not on to minimize any further delays. My thought was if it caught fire I could fight the fire like a laptop. After takeoff; I located the passenger/owner of the scooter and was told it was brand new and they were connecting to ZZZ1. I let [the] Passenger know it was onboard and that I would have them speak to a supervisor regarding what the procedure would be. Arriving in ZZZ I spoke to [the] Supervisor; she advised me I was not able to place it in the overhead bin but anywhere on the floor with sufficient space would've been okay. I'm writing this report to let the company know I had no idea and we should know this so it doesn't happen again.