The Lich King replaces the Night King in GOT Season 8. Who wins?

The Lich King thinks the Night King is a massive bitch and replaces him instead to take Winterfell and the rest of Westeros.

Setting:
- Takes place in the episode "The Long Night"

Lich King Conditions:
- LK is only with frostmourne
- LK is vulnerable to dragon-glass
- LK controls the white walkers (100,000)
- Can raise undead
- Cannot summon frost wyrms
- Cannot summon Valkyr

Westeros Conditions:
- Tirion Fordring leads a small coalition of 25 azerothian champions
- Dany has all 3 of her dragons + houses (128,000)
- The lannisters join them in Winterfell
- The dothraki don't charge in like idiots in the episode
- They all get buffed by Melisandre/Lord of Light

What's their strategy and can they stop the Lich King?