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?