There are actually several books in-game aimed at the specific classes that expand on one potential aspect of their fantasy. But you can't think of classes too narrowly from a lore standpoint; this isn't World of Warcraft.

Your "class" simply determines what kinds of magic your character has available to you. What I mean is that there are an extremely small number of people in Tamriel who call themselves "templars", but there are several organizations or professions that use holy, solar, and light-based magic. Priests of the Divines, crusader knights, and even certain Daedric cultists could easily fall under the Templar umbrella of class fantasy. The Resolutes of Stendarr come to mind.

Same with Dragon Knights. There are very few people in Tamriel that actually practice the ancient Akaviri martial arts, end even fewer who would call themselves "dragon knights", but there are many who use fire and stone magic.

Sorcerers are the best example of this. Almost all magica-focused characters in the world of Tamriel could fall under this umbrella fantasy, and yet very few would actually call themselves Sorcerers.

My point is that your "class" doesn't define your character in this game the way it does in many MMOs and other games. There' a ton of room for individual interpretation among all of them.