I think LCG L5R could be perfectly launched with 2 base sets. Let me explain:
Android: Netrunner Core Set comes with 7 factions and some neutral cards. In order to give many different playstyles with just the Core Set, some cards come three times, some two and a few come just once. So if you want to have 3 Desperado or 3 SanSan, you need three Core Sets, which gave you lots of unused cards, since as a general rule you can only have 3 times the same card in your deck.
Assuming max 3 copies of each card in a deck, L5R could be launched in 2 Core Sets (let's call them "Sun" and "Moon" just for fun with 4 clans in each set, with 3 times each clan card and two times each neutral card (economy, tutors, whatever...). While Sun and Moon have different clan cards, they share the same neutral cards. This way, if you want to be able to play with the eight clans, you just buy Sun and Moon (maybe not at the same time) and only one of each neutral card would be to spare.
It could be done with three differente Core Sets ("Sun", "Moon" and "Happy Vinegar Vampire") with just one neutral card of each kind in each set, but that looks much more difficult to sell, and buying just one Core would be pretty much unplayable. But I think launching the game in 2 Core Sets could be an option.