The question here would be, am I correct in saying that your conscience does bother you about eating meat - and so does every one elses'. As far as lions go, they learn from their parents to eat meat, it's not a pre-programmed reaction to hunger. You can also try contacting Tana Helfer, the daughter of the woman Toni Helfer who wrote the book The Gentle Jungle. Toni experimented with lions on a vegetarian diet and says they were all healthy. There are various other reports of the same thing with lions in different literature.
Animals kill, humans kill, that's a fact.
Your belief that it's not wrong and my belief that it is wrong are opinions. For your information, and this is a fact, I used to have an opinion similar to yours. Then I learned more and more how similar animals and humans are. Since I understand, being human, how I'd feel at the idea of some creature killing me and eating me, I learned to relate those feelings to animals. It doesn't take very much time when you're with an animal to realize that if you kill one, it can have a family which feels the loss and the sorrow.