If it’s a floating floor you can go over the existing floor if you want to… I know my wife would make me rip it out…

Luan in a bathroom is never a great idea. Actually I wouldn’t use it anywhere. Whatever you go over has to be flat. No bumps or dips. I’d like to say, because it’s a bathroom, 3/8” to 1/2” plywood, or better yet cement board. Patching compound on the seams.
I would start by removing all the 1/4 round and the toilet bowl. Maybe the baseboard too if it comes off easy. Under cut the door jambs. I would put it in lengthwise with my first full plank up against the tub only if it’s straight and square. It rarely is. You’ll probably have to scribe it. Just like with ceramic you want to do some measuring to avoid any little slivers anywhere if you can. That may mean ripping down your first plank. If the tub’s not straight and square you may want to snap a line and nail down a board or some blocks or something straight to start off of… Or you could run your planks across the width if that’s what your interior decorator wants… That would probably make for an easier install.