I don't think a lion is the appropriate symbol for the Lannisters. Because they glorify themselves as lions and they think because the lion is the king of beasts it makes them better than everyone. But the thing is the Lannisters always seem to die in the most embarrassing and shameful ways, like being killed on the toilet, walking naked through the streets, getting their hands chopped off. And Lions don't pay their debts. And also Wolves work together, dragons breathe fire, vipers have poison, bears stand their ground and flowers have thorns.