Lore can be seen as the back story. It might include details about the origins of a place, the past of characters, or the hidden histories that shape the current situation in a story or game.
The Lore TV show is indeed fictionalized. It takes elements from various sources and weaves them into fictional narratives that may or may not have real-world inspirations, but are not based on actual events.
Fictional lore is basically the background story and world-building in a fictional setting. It's made up of details like history, culture, and rules. For example, in the Lord of the Rings, the lore includes the history of Middle-earth and the different races and their powers.