I started playing season 1, but only started really paying attention to the lore around season 3.
I would still play if the threw out every single bit of lore, however my attachment to the game would be far weaker than it is now. The gameplay is enough to keep me playing, but gameplay needs can be fulfilled elsewhere, where as lore needs cannot. You can't just find a new story when you're invested in one already. Sure you can have multiple, but it's not always easy to give up that original one.
To put it as simply as I can if they cut the lore I would keep playing, but the moment my friends moved on to another game so would I. If there is a story, however, I'll come back time and time again.