Its hardly the player defining the world if its something that's already happened in game. If your adventures help lizardfolk, which is one of the most stock D&D plotlines to the point they invented Lizard Kings in previous editions to serve purely for that plotline, and it even shows up in Ghosts of Saltmarsh, and then want to play as them, what is stopping them from a storyline perspective? They've changed the world through their actions
If other humanoids like lizardfolk exist in the setting, then they should be able to become adventurers. That's the whole point of playing a tabletop RPG compared to just booting up Skyrim, far more freedom to do what you want rather than being stopped by the limits of the game
I get why I can't have a Lizardfolk adventurer in Neverwinter Nights (well, I technically can but
it hasn't been updated in over 20 years and most people prefer the later Lizardman model over the vanilla one), yet people managed to hook weimics into that game