I don't see any reason why you can't think you feel like (what you imagine) a lion feels like. It's your imagination etc.
And when someone tells me they identify as a Shark or a Lion or whatever else, I understand it's a metaphor and they're not really convinced they have a cartilaginous skeleton and live in the ocean etc. And for me that's as far as it goes and as far as I go.
Larping as a fur suit seems, well, a bit weird, but I'm down with weird. Generally larping is a harmless and wholesome hobby practised far away from non-participating people.
Woman who identifies as a wolf, meh. Why are we (general we) even talking about her and her eccentric hobby / imagination? Harmless eccentric, like Cowboy Joe who used to wander round my village shooting the kids with his finger guns, and if you shot him back, he'd pretend you shot him. (yeah it sounds a lot creepier that it was, he was a harmless old geezer)