Authority over motorsport activities comes from the local / national associations and they form a Federation (hence the F in FIA). Through this web they can sanction a large percentage of motorsport activity all the way down. If you don't accede to that authority then you can't race. A "rogue" series would be strictly limited on the tracks it could use for example.
So, that can't really apply to LFS. The only thing that could get in any way close is if the major leagues formed an alliance so they could pool resources (like marshals, servers etc), standardise rules and co ordinate race calendars etc. It would have anything to bind it together (like commercial interests) so it wouldn't be very cohesive, useful or longlasting.