Countering Leavanny
Pretty much any Steel Typed Pokémon, or any Fire Typed Pokémon. Notable choices from both types are Scizor, who can either outright OHKO Leavanny with its STABed Bug attacks, or set up Sword Dances as Leavanny is forced to switch or merely watch in horror. As far as fire types go, Heatran is a perfect counter, literally resisting any and everything Leavanny can throw it, barring a stray Hidden Power Ground. Other notable Counters would be Chandelure and Gengar, as they both resists pretty much everything Leavanny packs, though they must beware of a boosted Shadow Claw. Gengar, however can use disable on shadow claw to freely set up a substitute.
Infernape, Gyarados, Dragonite, Salamence, Garchomp, Gliscor, Excadrill, Landorus, Conkeldurr, Skarmory, Forretress, Ferrothorn and pretty much anything else that resists its stabs can freely use Leavanny as set up bait
Partners for Leavanny
Heatran is probably the best partner for Leavanny synergy wise as they resist each and everyone of each others weaknesses. Heatran can also get a nice Flash Fire boost off of Fire Typed attacks aimed at Leavanny. Heatran can also remove Scizor, which at least knocks one of Leavanny's hurdles down.
Leavanny isn't terrible at removing Psychic types and Bulky Grass / water pokémon, so anyone that is thankful for their removal, such as Conkeldurr, will appreciate Leavanny on the team.
Notable Moves on Leavanny
Leaf Blade, X Scissor, Reflect, Light Screen, Baton Pass, Agility, Swords Dance, Calm Mind, Hone Claws, Shadow Claw, Return, Leaf Storm, Flail, Bug Buzz, Hidden Power [Fire / Ground]
LC
Not sure if you actually do sets for LC, but if so:
Sewing Machine
Sewaddle (M) @ Life Orb
Trait: Chlorophyll
EVs: 132 Def / 196 SAtk / 180 Spd
Timid Nature (+Spd, -Atk)
- Calm Mind
- SolarBeam / Energy Ball
- Hidden Power [Fire]
- Air Slash / Bug Buzz
This would be used on a team with Vulpix support. After Chlorophyll boost, with the given EVs and nature it can outspeed Scarfed Gastly. Sewaddle will not be forcing any switches, but if you can bring sewaddle in on a Choice locked move like Thunderbolt from Gastly, you can set up Calm Minds. Solar beam is for sun abuse and STAB, Hidden Power Fire complements Solar Beam very well coverage wise, and gets a handle Pseudo-STAB boost from the sun, while the last move is down to preference. You can go Buzz Bug for Secondary STAB, or Air Slash for some better neutral coverage with a handy flinch chance.
Partners for Sewaddle would be Vulpix to provide sun support and to take the fire attacks Aimed at Sewaddle, they also have nice defencive synergy with each other, as Sewaddle can take water and Ground attacks aimed at Vulpix, whilst Vulpix can take the fire attacks Aimed At Sewaddle. However, they do both share a rock weakness. The rock weakness can be covered by Bronzor, however, Sun Boosted fire attacks will hurt even the sturdiest of Bronzor.