Former meat cutter weighing in here: In reality, meat gets worse when the animal is frightened before it’s killed. The given description of the physiological response to fear is pretty accurate, but it makes the meat tougher than it would be otherwise. It’s easiest to identify veal and pork where the animal “saw it coming,” it will be a much darker red than usual.
Who knows though, I guess it could be better for lions. It would taste more similar to how it would if they hunted the animal. The character has other strange ideas about what makes meat good (the white fur thing), so it makes sense from a narrative standpoint. Then again, why wouldn’t you want more tender meat?