Abrupt Decay: Despite this being very good removal it is one of the worst cards in the deck. Due to the nature of
Ensnaring Bridge, holding cards in our hand isn't something we want to do. This is best suited to take care of cards that can get around our lock,
Eidolon of the Great Revel,
Noble Hierarch, and
Cranial Plating are popular cards that come to mind to target if available. After sideboarding, this card gets a lot better by hitting
Stony Silence for us.
Academy Ruins: This card makes the whole deck run so smoothly. The ability to bring back artifacts we mill or get destroyed is so huge. It also enables an alternate win-con through Pyrite Spellbomb if the mill plan is going too slow.
Ancient Stirrings: One mana, search for a colorless card is amazing in the deck. These search effects, combined with our control of the draw steps mitigate the empty hand we are forced to play with. Stirrings helps us in the early game to find the lock pieces and in the late game they cement our lock even further.
Codex Shredder: Primarily, this is just a mill rock. However, the Shredder has a second ability that is extremely relevant and allows a lot of versatility in fetching any card out of our graveyard. Due to the slow nature of our deck we can loop non-artifact cards through Shredder and the Academy Ruins to an extremely debilitating effect.
Collective Brutality: This card is amazing, it does everything we could want and more. It stabilizes against aggro, kills problematic creatures, strips interaction from our opponent, and empties our hand for Ensnaring Bridge way faster than almost any other card. Most lantern players want to run 0-2 copies but I wouldn't be caught without at least 3.
Damping Sphere: This little artifact is what stands between victory and defeat in many of our worst matchups. It helps tax decks that want to double spell at a bare minimum, but where it really shines is against Tron. This can buy us the time we need to set up a proper lock on their draw step or to knock them out with flying Thopters before they crawl back into the game.
Grafdigger's Cage: This is the graveyard hate card that I picked but there are definitely alternatives which I will explain below. The reason to run Cage is it successfully stops reanimation, dredge, and flashback. In addition, it stops creatures from entering the library as well. Collected Company and Chord of Calling don't function under a cage. The important thing to remember is that Cage doesn't stop Living End.
Inventors' Fair: A land that can search our deck and gain us life is incredible. My only complaint is that it's legendary and I can't run more. This card is often the difference between life and death when you're up against Burn.
Lantern of Insight: In addition to the valuable information that it provides, the secondary shuffle effect can act as a psuedo-mill effect by getting rid of the worst card on top of their library.
Leyline of Sanctity: This is an all-star sideboard card. It improves our abysmal Burn Matchup, stops hand disruption, and if you're ever cursed to play in the mirror it turns off their Codex Shredder. A lot of Lantern players are running Leyline of Sanctity main board now, I am not a fan of this without at least 3 Collective Brutalities to pitch the extra copies. The Leyline is most effective against Discard and Burn and with the downward spiral Lightning Bolt has taken, I prefer filling my deck with other, more castable, cards.
Mishra's Bauble: This card is one of the more flex spots in the deck but it has so much synergy that it's hard to not include. The possibility of a cost artifact on T1 makes Mox Opal that much better, enabling more turns where we can play a colored spell on T1. It also acts as an emergency Lantern to get a one time peek at the top card of either players' deck. Usually the correct time to crack the Bauble is on your opponent's end step, as drawing a card on their turn is exceedingly detrimental and can cost you the game because of how Ensnaring Bridge functions
Mox Opal: This is a zero costing artifact that smooths out our mana and can help protect the risky turn 1 plays where your only land is a Glimmervoid.
Nature's Claim: One mana to destroy any artifact or enchantment is a really good deal. I bring this in whenever I think Leyline of Sanctity will be a problem along with any problematic card that Abrupt Decay can't hit. I've also found that cycling this card with Codex Shredder and Academy Ruins is extremely good against decks like Affinity and most Blood Moon decks.
Nihil Spellbomb: Helps give us an extra edge against graveyard decks. This makes Living End far more beatable and also helps beat up on Tarmogoyf and delve creatures like Gurmag Angler and Tasigur, the Golden Fang.
Padeem, Consul of Innovation: The only creature in our 75, she gives our artifacts hexproof and accelerates our lock by drawing cards. Bring her in for matches that have a lot of artifact destruction like Jund.
Pithing Needle: This card stops pretty much anything else that can operate under the lock. The two primary targets for it are usually Planeswalkers and Fetch lands but it can hit a number of creatures and cards. The important thing is to remember that it doesn't work on mana abilities and is thus mostly useless against decks like eggs.
Pyrite Spellbomb: Interaction with low toughness creatures that can be fetched and activated at instant speed thanks to Whir of Invention. I wouldn't ever run more than one, but it can make a big difference in the game. It also provides a way for us to burn the opponent out with Academy Ruins.
Seal of Primordium: This enchantment allows us to destroy other artifacts and enchantments without being forced to hold a card in our hand because of Ensnaring Bridge. Super useful if a little bit simple.
Search for Azcanta
: This is phenomenal filtering. It helps manage our draw steps on the front side so we can focus on the opponents and on the back side it can find almost every card in our deck. This definitely works better than Infernal Tutor and being repeatable is such a boon. It can seem weak at times but the deck wouldn't function without the consistency it adds.
Sorcerous Spyglass: Pithing Needle with half of Peek attached to it. A lot of people debate over whether this can be another normal Pithing Needle, but this can help determine the order of the needles you play. Which in a matchup like tron can be amazing.
Sword of the Meek: Like I said earlier, this card is next to useless without Thopter Foundry. On its own it can tap for improvise or count for metalcraft for Mox Opal and do nothing else. Since it comes back this is usually an easy mill given the choice.
Tezzert, Agent of Bolas: This is for the matchups where you suspect Stony Silence. He makes our artifacts useful again as a way to cause direct life loss or by making a bunch of 5/5s.
Thopter Foundry: This card adds another way to win for the deck and can also act as a poor substitution for an Ensnaring Bridge. Lantern is such an odd deck that people expect you to win in the weirdest ways possible like milling them out or looping Pyrite Spellbombs that they fail to expect and plan for you actually just attacking them with a swarm of creatures. This card also makes the burn matchup impossible to lose once you draw it since they simply cannot keep up with the lifegain. One important downfall to remember is that this card actually isn't colorless and thus cannot be grabbed by Ancient Stirrings.
Thoughtseize: The best discard spell in all of Modern. It can grab anything out of our opponent's hand on T1 for only one mana and 2 life.
Torpor Orb: This sideboard card helps shut down many problematic creatures like Snapcaster Mage, Ingot Chewer, Primeval Titan, Arcbound Ravager, and most of the 5C Humans deck.
Welding Jar: Artifact protection that doesn't need to stay in the hand and can be fetched by Whir of Invention? Absolutely! If the deck wasn't so tight I'd run more of these but I'd never be caught without at least 1 copy.
Whir of Invention: Lantern of Insight may be the namesake card of the deck and Ensnaring Bridge is the most important usually, but Whir of Invention is the most powerful card. This card represents every card in our deck and allows us to run as many silver bullets as we do. Even better, it helps bypass Meddling Mage and other effects like that by putting the card directly into play. Overpaying the X cost also doesn't limit what Whir can grab so it's a great way to disguise our true intentions. If I could run 8 copies of this card I would. It almost always only costs triple U because our deck is so good at improvising the rest of the cost.
Witchbane Orb: Hexproof for us is often the last piece needed to lock out the opponents and this lets us do it. Four mana can be a bit much but because we only run one its usually whirred for to get it directly into play.