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To kill a Lich the PCs must first destroy the lich's phylactery. From the Monster's Manual we know the basic physical description of this item:

A phylactery is traditionally an amulet in the shape of a small box, but it can take the form of any item possessing an interior space into which arcane sigils of naming, binding, immortality, and dark magic are scribed in silver.

It is possible for a given item to meet the physical description of the phylactery but not yet be activity used. I.e. The lich has not yet performed the ritual to bind their soul to the item.

What methods exist for the party to determine if an item is a phylactery?

Presumably the Identify spell will do the job but is that the only way? How long does it take for a given item? Particularly can a PC check multiple items at once or do all methods require a one by one approach?

For some context imagine the following scenario.

We know that liches are very protective of their phylactery:

Because the destruction of its phylactery means the possibility of eternal death, a lich usually keps its phylactery in a hidden, well-guarded location.

Given that liches are typically highly intelligent suppose they create a room to store their phylactery. After fighting past all of the physical and magical protections on this room the party is met with a room where dozens of objects sit on pedestals.

Each of these items meets the physical description of a phylactery, but only one is the true phylactery. In order to defeat the powerful lich the party must find the correct object and destroy it before the lich can complete its evil plan.

How can the players find the true phylactery as quickly as possibly?

The main question is asking for any possible way of determining if a given item is a phylactery. If there are multiple ways, preference is for the fastest (in terms of action economy) followed by lowest resource expenditure (spell slots, 1/rest abilities, gold) and finally by earliest availability (by class level).

A lich is exceptionally intelligent and careful, so this is likely to be a challenge. There are two main approaches:

• Use divination magic


• Use the unique properties of the phylactery to rule out which items cannot be the phylactery

Divinations

• 
  Commune (5th level) allows you to ask three yes or no questions. The optimal way to use this is what is known as a binary search. Suppose for example that there are 12 phylacteries:
  
  
  
  
  • Place the phylacteries around you in a clock pattern, with yourself in the middle, facing between 12 o'clock and 1 o'clock.
  
  
  • "Is the lich's phylactery one of the six to my left?" This will eliminate half of the possibilities.
  
  
  • "Is the lich's phylactery one of the three in front of me?" This will eliminate another half of the possibilities, leaving three remaining.
  
  
  • "Is the lich's phylactery the one I am touching now?" This has a 33% chance to get it right. If it fails, one of the remaining two must be it (unless they're all fake phylacteries, but that's still information worth discovering).
  
  
  
  


• 
  Divination (4th level) lets you ask one question, but you can use as a supplementary method if your commune failed to determine the exact phylactery and there are only two options left. Casting commune twice in one short rest has a chance to fail, but commune plus divination does not.
  
  
  
  
  • Another use of divination is as an opening question to determine if the phylactery is one of the items before you at all, in case your initial research leading to the phylactery room was flawed and they're all fake phylacteries. If they're all fake, you could use commune to help calculate the true phylactery's location and direction.
  
  
  
  


• 
  Legend lore (5th level) tells you facts about an item you name. The information you gain may be enough to narrow down the possible phylacteries.


• 
  Contact other plane (5th level) lets you answer five questions, but it's a dangerous spell to cast.


• Obviously, wish (9th level) or a cleric's Divine Intervention.

You can also try rolling an Intelligence (Arcana) check to see what information it gains, but it's up to the DM how much information this actually gives, and how much time it takes to research. There's a risk that the lich will re-constitute before you can even make it back to civilization to visit the library. Ideally, you want to do your research before you set out to destroy a lich.

Properties of a phylactery

• If the lich is killed, the lich only reappears within 5 feet the true phylactery. Place the phylacteries far apart, kill the lich, and see where the lich re-appears.


• A phylactery is typically not easy to destroy without some special method or equipment. Anything that is easily damaged can probably be discounted.


• A phylactery contains a soul, and also imprisons souls. If you had some way to detect souls or the movement of souls, you could use this property to detect the real item.


• A phylactery contains certain arcane sigils inscribed in silver upon its interior. Any item that doesn't is fake. The limit is that many phylacteries are opaque and nearly impossible to break, and therefore difficult to see inside without something like a ring of x-ray vision.

Spells that are unlikely to work

• You can't rely on identify, since a lich can easily have placed nondetection on it, which makes it immune to targeted divinations. Spells like commune still work, since they just ask another being for their knowledge.
  
  
  
  
  • The lich might also intentionally craft their phylactery as a cursed magic item, since curses cannot be identified by the identify spell.
  
  
  
  


• You can't rely on detect magic, since a lich can easily have placed a Nystul's magic aura spell effect on the real phylactery to mask its aura, or placed it on the fake phylacteries to give them fake auras.


• You can't rely on dispel magic to eliminate all the protections on a phylactery or dispel illusions on fake phylacteries. Since the permanency spell no longer exists in D&D 5th edition, the lich may choose to make nondetection permanent by enchanting the phylactery itself as a custom magic item with that property. In 5th edition, dispel magic only dispels spells, not magic items.
  
  
  
  
  • 
    Nystul's magic aura can be made permanent until dispelled, but a careful lich may still have made fake phylacteries as magic items which emit strong auras of necromancy, and again, items can't be dispelled with dispel magic.
  
  
  
  

In all of these cases, however, if you have these spells available it's worth a shot, in case either the DM is feeling reasonable, or the lich was so arrogant as to assume nobody could actually locate the correct phylactery, and failed to secure or maintain all of the necessary protections. Arrogance is a common NPC flaw (see DMG p.92).

If you are looking for the quickest, lowest expenditure of resources, and earliest availability, there is one answer for each of those, and that would simply be an Arcana skill check on an object suspected to be the phylactery. As it reads in the Player's Handbook (see page 177), emphasis mine

Arcana. Your Intelligence (Arcana) check measures
your ability to recall lore about spells, magic items,
e1dritch symbols, magical traditions, the planes of
existence, and the inhabitants of those planes

As described by the above description, it is usually used to identify rituals, identify magical items, recognize connections to magic, and basically anything else related to magic. For these same reasons, an Investigation check would not work if there are fake phylacterys (don't make that mistake when choosing what ability score to use), as quoted on Player's Handbook (see page 178), emphasis mine

When you look around for clues and
make deductions based on those clues. you make an
Intelligence (Investigation) check. You might deduce the
location of a hidden object, discern from the appearance
of a wound what kind of weapon dealt it, or determine
the weakest point in a tunnel that could cause it to
collapse. Poring through ancient scrolls in search of
a hidden fragment of knowledge might also call for an
Intelligence (Investigation) check.

So, whereas Investigation might find copies of the phylactery, as well as even the phylactery itself (which it can be useful for), the players won't know if it really is the real phylactery or not without an Arcana check

I would assume that "Identify" does the trick.

however; in the scenario OP posed (many options and time pressure), i would go for the faster option: destroy all items, and the stronghold as well, just in case