I'm on the pitifully chunky side myself right now- In the Clydesdale category, which is at 200 to 250 pounds last I heard- and fit tall strong. There isn't a hardtail made that will do 360 pounds, no fork will handle it. I'm not sure a Lifecycle will handle that either. Or that a gym will take her. My shop keeps fixing a heavy duty cruiser for a guy almost that heavy, he keeps breaking seatposts and snapping off pedal spindles.
Whith all seriousness, your freind is so big she may have trouble getting on a bike, then maneuvering it. An Adult Trike might be a good starter bike. The position tends to be towards the recumbent, Worksman makes a heavy duty one, and they work well with big tractor seats. And to be perfectly graphic- really big people have really big guts, this is a big fitting problem. I can't get on my road bike yet, and I'm at 210 after my long layoff, and I have a lot of muscle mass. When she gets a lot thinner and gets a comfort bike, trikes are great for parades and festivals. (you can haul a keg on one of those puppies!)
She really needs a checkup first, too. Hauling that much extra weight around is a huge cardio vascular strain even walking around the house. She probably hasn't exerted much in a long time, and you don't want her to hurt herself.

Lizzy