Guide
How the kit works
Start by setting up an element for Lynette to interact with. Use Enigmatic Feint for an Anemo strike: press it for a quick hit, or hold it to move quickly and mark a nearby opponent with Shadowsign. When the movement ends, Lynette approaches a nearby marked opponent before striking. You can end the movement early by using the skill again.
The strike heals Lynette when it hits, based on her Max HP, then she loses HP each second for the next 4 seconds. At specific intervals, the strike also releases an Ousia-aligned Anemo attack. Keep an eye on her HP rather than treating the skill as a replacement for a team healer.
Use Magic Trick: Astonishing Shift to summon the Bogglecat Box. It taunts, deals Anemo damage and can absorb Hydro, Pyro, Cryo or Electro once during its duration. After absorption it fires Vivid Shots of that element, and a passive gives Lynette's Burst 15% more damage until the box expires. Another passive grants the party 8% to 20% ATK for 10 seconds after the Burst, depending on the number of different elemental types in the party.
Build and why
Use four pieces of Viridescent Venerer for a Swirl support build. The set increases Swirl damage by 60% and reduces an opponent's RES to the element infused in Swirl by 40% for 10 seconds. Lynette's Burst keeps dealing Anemo damage, giving her a way to use the set while the box is active.
For a Burst damage build, consider four pieces of Emblem of Severed Fate: its two-piece bonus gives Energy Recharge, and its four-piece bonus converts part of that stat into Burst damage. Four pieces of Noblesse Oblige are another option for a team that wants ATK; using the Burst grants the party 20% ATK for 12 seconds, and the set's two-piece bonus also increases Burst damage. Four pieces of Instructor are worth considering for its party Elemental Mastery buff after a reaction.
For main stats, consider Energy Recharge or Elemental Mastery on the sands, Elemental Mastery or Anemo DMG Bonus on the goblet, and Elemental Mastery, CRIT Rate or CRIT DMG on the circlet. ATK Percentage is another sands option. Prioritize Energy Recharge in substats, followed by Elemental Mastery, CRIT Rate, CRIT DMG and ATK Percentage.
Favonius Sword is the first weapon choice: CRIT hits have a chance to generate particles, so give Lynette enough CRIT Rate to make use of it. Sacrificial Sword can reset the Skill's cooldown after it damages an opponent. Freedom-Sworn is another option; its listed effect increases damage and gains Sigils when its wielder triggers reactions.
Leveling priority
For a support build, I'd level Magic Trick: Astonishing Shift first because the box deals damage at intervals. Follow it with Enigmatic Feint, then Rapid Ritesword (NA). Move Normal Attacks up if you spend more time attacking with Lynette, particularly with her sixth constellation.
For maximum character ascension, prepare 420,000 Mora, 168 Lumidouce Bell, 1 Vayuda Turquoise Sliver, 9 Vayuda Turquoise Fragment, 9 Vayuda Turquoise Chunk and 6 Vayuda Turquoise Gemstone. You also need 18 Meshing Gear, 30 Mechanical Spur Gear, 36 Artificed Dynamic Gear and 46 Artificed Spare Clockwork Component — Coppelia.
To raise all three skills to their maximum, prepare 4,957,500 Mora, 3 Crown of Insight, 9 Teachings of Order, 63 Guide to Order, 114 Philosophies of Order, 18 Meshing Gear, 66 Mechanical Spur Gear, 93 Artificed Dynamic Gear and 18 Everamber.
Constellations worth it
Watchful Eye is the biggest change: after Enigma Thrust, Lynette gains Anemo Infusion and 20% Anemo DMG Bonus for 6 seconds. It gives her a reason to stay on the field and use Normal Attacks after her Skill.
Among the earlier upgrades, A Cold Blade Like a Shadow is worth considering for grouping. Its vortex appears only when Enigma Thrust hits an opponent marked by Shadowsign, so use the held Skill and reach the marked target. Tacit Coordination is another useful option because it adds a Skill charge.
Endless Mysteries makes the box fire an extra Vivid Shot each time it fires one, so it needs the box to absorb an element. Cognition-Inverting Gaze and Obscuring Ambiguity add levels to the Burst and Skill respectively. You can skip aiming for those level increases if you are content with Lynette's support tools.
Teams
Pair Lynette with a damage dealer who benefits from reduced Hydro, Pyro, Cryo or Electro RES when she uses Viridescent Venerer. Neuvillette is a Hydro option, while Arlecchino is a Pyro option. Make sure Lynette triggers Swirl with the element whose RES you want to reduce.
Furina or Xingqiu are options for a Hydro slot, and Fischl is an Electro option for a team that wants another element. The box can absorb only one element per use, so pay attention to which one reaches it if its Vivid Shots matter to your plan.
Bennett is a Pyro teammate to consider, while Zhongli provides a shield option. Lynette heals herself with her Skill, but it does not heal the rest of the party. Different elements also increase her passive ATK buff: a party with four elemental types gets 20% ATK for 10 seconds after her Burst.
Common mistakes
Don't expect the held Skill to chase a marked opponent from any distance. Only one opponent can carry Shadowsign, and the mark disappears if that opponent gets too far away. At C1, missing the marked target also means missing the vortex.
Don't forget the box can absorb an element only once. If it absorbs the wrong one for your plan, its Vivid Shots will keep that element for the rest of that use. For Viridescent Venerer, check the element involved in Lynette's Swirl rather than assuming any Anemo hit reduces the RES you want.
Don't neglect Energy Recharge when building around the Burst. If you use Favonius Sword, remember that its particle effect needs a CRIT hit and has a chance to activate. Also watch Lynette's HP after her Skill: the healing on hit is followed by HP loss.