Quake. At the start of your turn the ground falls our from beneath a random enemy within 60ft. They must make a dexterity saving throw or fall prone hanging onto the ledge.

Remorseless Winter. The biting cold surrounds the Lich King and any creature that starts their turn within 10ft of him takes 5 cold damage.

Necrotic Plague. When any undead summoned by the Lich King dies, the spread a plague of undeath. The closest creature to the undead becomes infected with the necrotic plague  and must make a constitution saving throw at the start of their turn. If they fail, they take 5 poison damage. This effect continues until the make a successful save at the start of their subsequent turns. This effect can stack increasing damage by 5 for each stack.

Frostmourne Hungers. Any creature brought to 0 hit points by Frostmourne but make a constitution saving throw or have its soul sucked within the blade, immediatley killing it. 

Spellcasting. The Lich King is an 11th level spellcaster. Its spellcasting ability is Charisma (spell save DC 18, +8 to hit with spell attacks). The Lich King has following spells prepared:

Cantrips (at will): Chill Touch, Eldritch Blast, Frostbite, Ray of Frost

1st level (4 slots): Armor of Agathys, Command, Dissonant Whispers, Wrathful Smite

2nd level (3 slots): Crown of Madness, Enthrall, Misty Step, Rime's Binding Ice

3rd level (3 slots): Animate Dead, Counterspell, Dispel Magic, Fear

4th level (3 slots): Blight, Dimension Door

5th level (2 slots): Dominate Person, Cone of Cold

6th level (1 slots): Freezing Sphere 

Multiattack. The Lich King makes 3 attacks with Frostmourne

Frostmourne. Melee Weapon Attack: +10 to hit, reach 5 ft., 1 target. Hit: 13 (2d8 + 4) slashing damage + 9 (2d8) necrotic damage.

Death Coil. Ranged Spell Attack: +8 to hit, range 60 ft., 1 target. Hit: 36 (8d8) necrotic damage and heals the Lich King for half the damage it deals.

Death Grip. The Lich King grips a creature he can see within 60ft with necrotic energy. The creature must make a strength saving throw or be pulled next to the Lich King.

Necrotic Smite. When the Lich King hits with a melee attack he can smite the target dealing an addition 4d8 necrotic damage.

The Lich King can take 3 legendary actions, choosing from the options below. Only one legendary action option can be used at a time and only at the end of another creature’s turn. The Lich King regains spent legendary actions at the start of his turn.

Frozen Shift (Costs 1 Actions). The Lich King casts Misty Step

Frostmourne (Costs 2 Actions). The Lich King makes an attack with Frostmourne.

Death Coil (Costs 3 Actions). The Lich King makes a Death Coil attack.