the quiet night
Lantern Night is the one night the game gives you nothing to fight. No invasion, no forced boss, no spawn changes beyond the usual dark: paper lanterns drift up through the background and that is the whole visual. The reason to care is luck. Every player gets a flat bonus of 0.3 luck for the entire night, applied everywhere at once with nothing to drink and no torch to place, which is a larger single push than most luck sources manage. Wind also falls to nothing while it runs, so trees and hanging furniture go still.
The Party Girl adds the Release Lantern to her stock for the night if you want to throw your own into the sky.
what schedules one
Kill any boss for the first time and the following night is a Lantern Night. The same holds for the first clear of any invasion. There are carve-outs: the Pumpkin Moon and Frost Moon do not count as invasions for this, though the first Pumpking or Ice Queen kill does trigger one, and Mourning Wood, Everscream and Santa-NK1 never do. The Eater of Worlds counts as the same entry as the Brain of Cthulhu, so whichever world evil you rolled, only the first kill across that pair pays out.
In practice the early game hands you a run of them, one per new boss and one per new invasion, and then they stop. After the Moon Lord dies they come back as a random event instead, with a 1 in 14 roll each night and a forced gap of 5 to 10 nights after each one that succeeds.
Only one scheduled Lantern Night can be queued at a time. Kill two first-time bosses between one nightfall and the next and you still get a single night out of it, so spreading first kills across separate days is worth doing if you want the luck more often.
delayed, not canceled
If a boss is alive, an invasion is running, or a Blood Moon or one of the moon events is up when the sun goes down, the Lantern Night does not fire that night. It moves to the next one. Nothing is lost by clearing a boss and immediately starting something else, so there is no reason to sit on your hands waiting for the reward. The same applies after Moon Lord: if a random roll succeeds on a night that already had one scheduled, the random one runs and the scheduled one waits until tomorrow.
What does kill it outright is starting something in the middle of the night. Summon a boss or trigger another event while the lanterns are up and the night ends for good, even if the boss despawns a minute later. Save the summons for morning.
spending the luck
Luck shifts drop rolls and rare spawn rolls in your favor, so the night belongs to whatever you have been grinding without result. Rare enemy drops, statue farms sitting on a low percentage item, fishing for an uncommon catch, anything with a long tail. Stack it with a Luck Potion and the right torch for the biome you are standing in and you are running about as hot as the game allows.
Enchanted Nightcrawlers can also spawn naturally during a Lantern Night, but only if a Starfall is happening at the same time. When the two line up, walk your grass with a Bug Net and stock up on high tier bait you would otherwise be buying.
the spawn side effects
The peace has a price. While a Lantern Night is active the Eye of Cthulhu will not spawn naturally and neither will any mechanical boss, so if you were counting on one turning up while you build, it will not. A Lantern Night that lasts all the way to dawn also stops a Goblin Army, a Pirate Invasion or a Solar Eclipse from starting that morning. Anyone farming invasions should treat a lantern night as a lost cycle.
where the idea came from
The event was shown off during development as a nod to the lantern release scene in Tangled, which itself borrows from the Chinese lantern festival that closes out the new year celebrations.