Gryffindor: Why the Lion?
So... why the lion? It seems like an obvious choice, no? A king of beasts, fearless? But let's take a step back and appreciate all that is Gryffindor's house animal.
From my other post regarding Hufflepuff, we know that the house animals seem to represent various parts of the UK, with Scotland represented by the noble red lion, so this leads us to a few interesting questions, and prodding that honestly makes almost no sense in analyzing, but we're gonna do it anyways.
First is the obvious question, of Godric's Hollow. I realize it is a strange thing to bring up, but it almost needs to be said. Godric was born in.... England! Yes, after doing more research as to the location of Godric's Hollow, it was located in England. However, Ravenclaw was Scottish, referring to her in Goblet of Fire as being "from the glen." Odd, but it's worth correcting slightly, ruining the founders being from the locations the animals were from, but rather the House animals still representing the union of the UK, albeit in a subtle way.
We also have the connection to the griffin in Godric's name, a combination of the eagle and lion, fitting for the Griffindor common room's high location, but questionable to why the griffin is not the animal, as opposed to the lion. This can be split up in two arguments (dismissing the UK theory), one, that the griffin is not a traditional griffin but a golden griffin, a pun on griffin d'or (french), second, that the griffin just wasn't the right fit. Compare it to the lion, a symbol for courage, while the griffin does have a similar stature as brave, it is more of a protector in certain uses, and interestingly enough, the griffin we think of in mythology is the female griffin of the middle ages (the males did not have wings and had a tusk, though more likely than not, Rowling put it as a "traditional" griffin). Furthermore, it could be that the founders chose "muggle" creatures as to better hide the symbolism of their house, and protect those in the school from being labeled based off of the possession of a banner or symbol for the house.
Thus, we see that the lion is an obvious choice, but also a well thought choice. It represents a part of the UK, serves its purpose of providing symbolism of bravery and regal behavior, and does so better than the griffin.