Hi :-) I'm not sure what philosophy "it doesn't seem possible to apply universally".. Maybe "Killing any animal is wrong" (By any animal/person, for any reason, etc)? I don't think that. Also, I don't see this as an "argument in favor of eating less meat", or a "moral requirement".. Is it hard for you to not hunt, kill and eat people? Do you need arguments in favor of having less slaves. No.. Those things seem morally repugnant to most of us now, while they were normal in other times and places.
Two points from the many that bear on this:
1. The line between "humans and uh cats and dogs" and everything else seems arbitrary, human-centric etc. "Those in my group have value, those outside are nothing" comes naturally to humans, but there's nothing reasonable about it. For me, I don't like pain. I think inflicting pain/suffering is bad--not to mention painless killing, which seems worse than inflicting suffering. I would prefer someone inflicted pain on me than killed me painlessly! (How strange that I felt the need to explicitly make that point.)
There is a range of life-forms on this planet, from simple to complex, some of which, like single-cell bacteria, viruses, probably don't feel pain. (Neither do trees, it seems--they can't run away so it didn't evolve. But I respect them for other reasons. I hate seeing heavily graffitied trees, I wonder who could do that desecration.) There seems no obvious line to draw between animals whose pain/suffering, and lives, are worthy of ethical consideration, and those whose aren't. (And conveniently, we put humans at the top of that range, presumably other animals might see things differently) Doctors/vets kill lower-life forms to save higher ones. Personally, I put it fairly low (Oysters?..).. but to save worrying about the exact place to draw the line, I've found it simpler (and painless, I've never missed 'it') to avoid animal products altogether.
2. The matter of need. If it's a matter of killing animals for food or dying, I would do the same. (or even eating people, see the movie Alive.) If it's a matter of, for you and I, wanting a steak, when there's no need whatsoever, it's an entirely different thing. I stopped dairy products when I learnt about what people do to cows and their babies in that industry. And learn about factory farming of chickens, pigs, cows, go on a tour of an abattoir--the gruesome realities are hidden from us.
Also, I'm just talking about ethical considerations for humans, how we treat other life-forms. Because we realize other people than ourselves matter, other species than ourselves. (Not really sure what to say about the lions in your example.)