The FWG Core in LC
While Little Cup is often thought of as a balanced or offensive metagame, defensive cores are actually more prevalent than even most LC players realize. The core of a Fire-, Water-, and Grass-type is quite common in other tiers, but it isn't always seen in LC because poor renditions of such a core struggle against status effects and Fighting-types, the most prevalent offensive threat in the tier. Nonetheless, a properly built core can typically stall teams late game and still provides a well rounded batch of resistances that can be useful in the early phases of team building.
It can be difficult to find a good "Fire-type" in LC, so it’s wise to choose this slot first. Larvesta is easily one of the best choices, as it threatens all Mienfoo lacking Stone Edge due to Flame Body. It also provides offensive momentum in the form of U-turn. Ponyta trades the Fighting-type resistance for less of a crippling Stealth Rock weakness and typically greater power and Speed. Houndour is the epitome of the offensive Fire-type, cleaning up late game but not offering much in the way of defensive prowess. Each choice marks a decidedly different type of play style and also sets the general direction for the rest of the team.
If one opts for Larvesta, Staryu then becomes almost a given, as Rapid Spin support is all but essential. Staryu also has that great Speed stat of 19, access to Thunderbolt to scare off Murkrow, reliable recovery, and a surprisingly strong Hydro Pump. Chinchou also works well if Rapid Spin support can somehow be dealt with, sporting a resistance to Murkrow's STAB Brave Bird and is capable of synthesizing the VoltTurn combo that is "unbeatable" according to most scrubs on Pokemon Showdown. Both of these choices give a lot of leeway for the final member of the core, the Grass-type. Shroomish is useful as it deals with Drilbur most of the time. One can often afford to use Lileep or Ferroseed, two Pokemon weak to Fighting-types, if they are paired with Larvesta, as Mienfoo will have to play conservatively if it wants to avoid a burn. In conjunction with the aforementioned VoltTurn strategy, these two Pokemon can provide Stealth Rock (and Spikes, in Ferroseed's case) support to give the opponent a headache.
Ponyta, despite also having Flame Body, still marks yet a different aim in team building. Whereas Larvesta, despite being an offensive Pokemon, takes the team in a defensive direction, Ponyta is more of a middle road towards balance. Another Fighting-type resistance is all but required, and Slowpoke, Frillish, or Foongus are all good options. Slowpoke baits U-turn from Mienfoo endlessly, which often means a free switch-in for Ponyta. Frillish can spread Toxic while maintaining good coverage with its STABs, taking on weakened Misdreavus and in general, sticking around with Recover. Foongus is not to be neglected as a Grass-type, thanks to its ability to spread status. If Foongus is used, one can even go for a more offensive Water-type, such as Choice Scarf Chinchou or Staryu. If Foongus isn't used, Lileep remains a solid choice for a Grass-type. Even Chikorita could be considered for its abilities as a cleric.
Yet maybe you'd rather take the road less traveled by and go with Houndour; indeed, that may make all the difference. Houndour marks an offensive approach to the FWG core. Slowpoke is again a good choice for the Water-type, as whatever you choose needs to be able to repeatedly soak hits from Fighting-types and Ground-types; Regenerator allows Slowpoke to do just that. If you decide on Life Orb Houndour, Staryu becomes a viable option, providing Rapid Spin support to minimize Houndour's residual damage. Many traditional Grass-types, such as Lileep and Ferroseed, are weak choices alongside Houndour as they compound its weakness to those ubiquitous Fighting-types. Instead, Foongus could be considered, as could Shroomish or even Bulbasaur due to its access to Knock Off. One could even decide not to allocate the Grass-type slot to a defensive Pokemon at all; Snover is certainly viable as an early game cannon to pair well with Houndour's late game job as janitor, although then you begin to delve into the realm of hyper offense where only a few people ever go.
While it is difficult, FWG cores can often be a good starting point for a new team. And while the options may seem limited here, you should by no means take this as a completely exhaustive list; after all, experimentation is a spice of life. Hopefully even people from other tiers are now rife with new LC ideas, even if the Fire / Water / Grass seems greener on the other side.