There are two known types (species, perhaps) of lions in Ice and Fire, the lion of the Westerlands and the hrakkar - the white lions of the Dothraki Sea. read more
Yes, obviously they do. Here’s the wiki entry: Lion. In Westeros, lions mainly inhabit the westerlands. That it why the two most prominent families of that region, the Lannisters and the Reynes, both have a lion on their banners. read more
It's been a long, long time since a certain character has been to Winterfell, but new spoilers suggest Game of Thrones season 8 could change that. read more