How does the Lich's Tether Lair Action interact with damage resistance?

Question

The Lich has the Lair Action:

The lich targets one creature it can see within 30 feet of it. A crackling cord of negative energy tethers the lich to the target. Whenever the lich takes damage, the target must make a DC 18 Constitution saving throw. On a failed save, the lich takes half the damage (rounded down), and the target takes the remaining damage. This tether lasts until initiative count 20 on the next round or until the lich or the target is no longer in the lich's lair.

The Lich also has various damage resistances and immunities. I originally thought that the target would only have to save if the Lich actually takes damage, ie if the damage makes it through the Lich's resistance.

However, looking at this answer it seems that damage resistance is applied after all other reductions, therefore, the target needs to save against the full original damage. Only after that half of the damage has been "redirected" would the Lich then apply resistance to the remainder.

For example, my Lich uses this Lair Action on initiative count 20, tethering itself to the party Wizard. The party Fighter then, armed with a mundane sword, attacks and hits the Lich, dealing 8 non-magical slashing damage. In this case, does the Wizard have to make a constitution save or take 4 damage? Or, does the Lich resist all the damage, effectively taking no damage, negating the need for the Wizard to make a saving throw at all?

Answer 1

Going off the phrasing of the effect

When the Lich takes damage

Not "When the Lich is hit with an attack/spell/etc," when they take damage.

In this case, a Lich's resistances and immunities are applied before you determine whether or not Tether fires off. Because until you apply those, the Lich hasn't taken any damage yet.

So, since when you hit a Lich with a nonmagical sword they take Zero Damage, then even if you still ruled that Tether activated, then the Wizard would have to save against taking half of zero damage...so, no damage at all.

The specific wording you are referring to of

Resistance and then vulnerability are applied after all other modifiers to damage

Are all still applied before a creature actually takes any damage. It's not like a Fire-immune creature gets hit with a fireball, takes the fire damage, and them immediately heals that damage. They simply don't take any damage at all.