Does Legendary Resistance allow a Stunned or Paralyzed creature to succeed on a save it would otherwise automatically fail?

Question

Both the Paralyzed and Stunned conditions include the following:

• a [paralyzed/stunned] creature is incapacitated (see condition) and can't move (or in the case of paralyzed speak)
• The creature automatically fails Strength and Dexterity saving throws

The Incapacitated condition specifies:

• An incapacitated creature can't take actions or reactions

Some creatures, such as Dragons, have Legendary Resistance:

Legendary Resistance (3/Day). If the dragon fails a saving throw, it can choose to succeed instead.

Legendary Resistance does not require an action or reaction, so the Incapacitated condition does not seem to prevent its use.

RAW, there doesn't seem to be anything preventing an incapacitated, paralyzed or stunned creature from "choosing" something that doesn't explicitly require any kind of action.

[Perhaps the question is moot anyhow because if a creature had legendary resistances left, they probably would not allow themselves to be incapacitated.]

Answer 1

Yes, the Legendary Creature could still use Legendary Resistance while stunned or paralyzed.

General Rules:

Stunned

• A stunned creature is incapacitated (see the condition), can’t move, and can speak only falteringly.
• The creature automatically fails Strength and Dexterity saving throws.
• Attack rolls against the creature have advantage.

Paralyzed

• A paralyzed creature is incapacitated (see the condition) and can’t move or speak.
• The creature automatically fails Strength and Dexterity saving throws.
• Attack rolls against the creature have advantage.
• Any attack that hits the creature is a critical hit if the attacker is within 5 feet o f the creature.

Incapacitated

• An incapacitated creature can’t take actions or reactions.

Creature Ability:

Legendary Resistance (3/Day).

• If the dragon fails a saving throw, it can choose to succeed instead.

It shouldn't matter whether the failure of the save was due to rolling or if it was automatic. The ability allows any failed save to immediately be converted into a success three times per day. Also, since Legendary Resistance is not an action, being incapacitated should have no effect.

While it is unlikely that a legendary creature would allow itself to become stunned if it still had uses of Legendary Resistance remaining, there could be a game effect which stuns the creature without allowing for a save (such as critical/fumble decks or tables) or the creature may have made a poor choice and allowed it. In such cases, I believe that the creature could still choose to use their ability while stunned.

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@Erudaki pointed out that Power Word Stun is very relevant to this answer. it is an 8th level spell with no initial save (as long as the target has 150 hp or less remaining). The target does get to make saves at the end of each of its turns.

Answer 2

I think we would be right to assume no legendary creature would allow itself to be paralyzed or stunned while still having legendary resistance uses remaining.

By RAW I would say Legendary Resistance overrides Paralyzed/Stunned, because the creature first fails the save, then chooses to succeed at it (that's how I understand the rules would stack, and Paralyzed/Stunned doesn't mean unconscious).

And as I see it, Legendary Resistance was intended to represent how "awesome" these creatures are by virtue of them just being (dragons, vampires, the tarrasque, etc) and how that means they just shake off certain effects without a second thought. Being Paralyzed/Stunned doesn't take away that awesomeness, though it dampens it a little.