You feel oddly distant at the news that you're a part of this creature's digestive tract. It's better than being digested, but worse than if you were outside of his body and able to run free. The sheer stupidity of the thought gives you a sensation similar to holding a pair of fluttering wings, but your host doesn't seem to notice it; you'd probably have 'run free' straight into the mouth of another predator like the one you're currently inside. That raises another question; why did he look so happy to see you, only to do... this? Is it anything to do with that hyena he was talking to?
You feel the sensation you've learned to associate with walking stop. You hear a few sharp bellow-breaths from the nearby lungs, and then a deep 'hrrmff' and the rocking motion of the lion-man's stride begins again.
Hours pass. You're pretty sure it's hours. It couldn't have been days because you haven't slept yet, and there are only so many things you can do with the sensory information coming to you from the lion-mans gut. The only change to the monotony is that every so often he'll stop, take a few sharp breaths, make a noise and carry on walking. Once, you feel him crouch down, muscular body folding around you, and feel liquid running into you from his throat. The moment is all-too-brief, as something makes a loud noise and you feel his muscles spring into action around you. You hear water, and then silence as the lion-man's abdominal muscles relax.
He says something. You have a front-row seat to the auditorium of his voice, so it's not that you didn't hear; rather you simply can't understand the guttural noises that he makes. You feel an odd motion around you, and then the movement that means 'walk', only sped up. A short while later and you feel him crouch, stand, move, crouch again and then, finally, feel water coming from his throat until you get the sensation of being a slightly over-filled balloon.
You're not entirely sure how to deal with this. You know that, in theory, water needs to be somewhere not in the stomach. You've drank plenty of soda, tea and coffee, and never once thought about how it gets from in your stomach to elsewhere. The sensation of your lionish host walking away from the scene of the crime comes secondary to working out what to do with-
Oh.
Without you really noticing, you've started to feel less full. You think about things a bit, and decide that water would probably be the easiest thing to digest. It leaves you vaguely worried about what'll happen when actual eating happens; there's no way you'll work out how that whole thing works.