Can monsters use lair actions on targets in any part of their lair?

Question

My previous experience with Lair Actions has been when the party fought Strahd (a vampire lord in Curse of Strahd) and Arauthator (an adult white dragon in Rise of Tiamat). Both of these creatures had multiple Lair Actions, but all of the actions either specified that they only applied to the creature (Strahd / Arauthator) itself or to a target it could see.

My party will soon be facing a mummy lord (for the particular mummy lord and circumstances of its lair, see this question, but be aware that even the question title contains spoilers). The mummy lord's lair actions are:

On initiative count 20 (losing initiative ties), the mummy lord takes a lair action to cause one of the following effects; the mummy lord can’t use the same effect two rounds in a row.

• Each undead creature in the lair can pinpoint the location of each living creature within 120 feet of it until initiative count 20 on the next round.
• Each undead in the lair has advantage on saving throws against effects that turn undead until initiative count 20 on the next round.
• Until initiative count 20 on the next round, any non-undead creature that tries to cast a spell of 4th level or lower in the mummy lord’s lair is wracked with pain. The creature can choose another action, but if it tries to cast the spell, it must make a DC 16 Constitution saving throw. On a failed save, it takes 1d6 necrotic damage per level of the spell, and the spell has no effect and is wasted.

Note that none of these Lair actions refer to the mummy lord itself or explicitly state that it needs to see the target of these effects.

This is particularly relevant to the specific mummy lord in question, as it does not leave its room, but its lair itself is large; players would have a chance to be affected by all three lair actions at some point during their exploration of the lair even while not in the physical presence of the mummy lord (if that is possible).

The answers to this question all state that a monster must be present in its lair in order to take lair actions, because it is the monster itself taking the actions, and I agree with that. This answer in particular states that since the Lair Actions happen on Initiative 20, and are taken by the monster, the monster must be part of the Initiative order, and I agree with that as well.

While it could be argued that a mummy lord that did not leave its room would not be part of a combat in another room, and thus would not be in the initiative order, I think that argument is circular. I could just as easily say that the Lair Actions themselves make the mummy lord part of a combat even if it is not physically present by providing it with actions that can affect the course of the combat, so that the mummy lord is placed in the initiative order of every combat in their lair even they are not physically present and even if their only action each round is to take their Lair Actions on Initiative 20.

Can monsters use lair actions on targets in any part of their lair, even when they are not in close proximity and even when they cannot see the targets?

Answer 1

Depends on the lair. Maybe.

I wasn't able to find any general rules for this -- the closest is this statement in the Monster Manual section on Legendary creatures:

A legendary creature might have a section describing its lair and the special effects it can create while there, either by act of will or simply by being present.

So this could be read as meaning "As long as a creature with lair actions is in its lair, then it may take a lair action each round at initiative count 20". By extension, any lair action that doesn't require a target could be taken even if the monster isn't aware of any other creatures in its lair.

So when is a creature "in" its lair? That depends on the lair. For many creatures, the lair is a single (presumably large) chamber:

Beholder:

A beholder’s central lair is typically a large, spacious cavern with high ceilings.

Black Dragon:

A black dragon’s lair is a dismal cave, grotto, or ruin that is at least partially flooded

Bronze Dragon:

A bronze dragon lairs in coastal caves.

Copper Dragon:

Copper dragons dwell in dry uplands and on hilltops, where they make their lairs in narrow caves

Green Dragon:

At the center of its forest, a green dragon chooses a cave in a sheer cliff or hillside for its lair

Kraken:

A kraken lives in dark depths, usually a sunken rift or a cavern filled with detritus, treasure, and wrecked ships

For these creatures, the boundaries of the chamber constituting the lair are probably straightforward.

For others it's a larger complex:

Sphinx:

A sphinx presides over an ancient temple, sepulcher, or vault

Lich:

A lich often haunts the abode it favored in life, such as a lonely tower, a haunted ruin, or an academy of black magic.

Here the lair could be a building, dungeon complex, or even several structures.

For a Mummy Lord:

A mummy lord watches over an ancient temple or tomb that is protected by lesser undead and rigged with traps.

Note that the lesser undead are in effect part of the lair for the mummy lord, and that their lair is likely far more extensive than the range of their direct senses. So it seems reasonable that a mummy lord can activate any of its lair actions at any time -- a DM might rule that at the start of any combat, a random one of the three lair actions is in effect for the first round. As soon as the mummy lord is aware of the combat (by using its first lair action), it will choose which action to use each turn.

Answer 2

Yes, unless the action requires the monster to see the target.

Red Dragons need to see their targets to do things:

Magma erupts from a point on the ground the dragon can see within 120 feet of it

Volcanic gases form a cloud in a 20-foot-radius sphere centered on a point the dragon can see within 120 feet of it.

The Mummy Lord does not:

Until initiative count 20 on the next round, any non-undead creature that tries to cast a spell of 4th level or lower in the mummy lord's lair is wracked with pain.

The Sphinx needs for some and not for others:

The flow of time is altered such that every creature in the lair must reroll initiative. The sphinx can choose not to reroll.

The sphinx shifts itself and up to seven other creatures it can see within in its lair to another plane of existence.

So when a combat starts in a monster's lair, the monster is part of initiative (even if not in the same room), unless the monster is not aware of what's happening in the lair (or they're unconscious or something). Narratively, this means that the boss is aware of intruders, and controlling its territory against them. For each specific action, check whether it states the target must be seen by the monster or not, and use it as needed.

For the Mummy Lord specific case, no sight is required.

Answer 3

No, or not without a good reason

Consider this quote from the rules for legendary creatures:

Lair Actions

If a legendary creature has lair actions, it can use them to harness the ambient magic in its lair. On initiative count 20 (losing all initiative ties), it can use one of its lair action options. It can't do so while incapacitated or otherwise unable to take actions. If surprised, it can't use one until after its first turn in the combat.

That last sentence is a fair indicator of how lair actions work. The creature only uses them after they become aware of the presence of enemies and can start acting. They don't just keep triggering them every 6 seconds for no good reason.

Another thing to consider is what the definition of a lair actually is. I haven't read the source material you are using, but I'd have thought it would only be the room where the creature is actually located, not the building/dungeon where it resides.