Sekiro: Where To Find Lapis Lazuli
One of the most difficult resources to find in Sekiro: Shadows Die Twice is Lapis Lazuli. You use this to upgrade your Prosthetic to receive higher quality Upgrades when you speak to the Sculptor. What makes this resource so challenging to find is because of how you go about looting it. It comes in a variety of limited sources, and some of them you have to work extraordinarily hard. However, many of these tasks are closer to the end of the game, so you should feel comfortable enough with Sekiro to tackle them.
Where To Loot Lapis Lazuli
The first location we're going to find this incredibly rare resource is in the Fountainhead Temple. You have to run past the first section and jump over the broken bridge where you first encounter a far-off in the distance individual who is throwing lightning at you. Ignore them, and proceed to the right side of the temple towards the waterfall. You should see it peaking through the exposed temple. You'll want to choose between taking out the numerous guards, or avoid them as you head over.
When you're there, you're going find a few demented dogs hovering around an item. Take them out, and you should see the fourth one among the cliffs to the right. Kill it, and remain crouched. Go to the highest point of the rock side and lean over, where you should see the Shicimen Warrior, a mini-boss underneath the waterfall. Make sure you activate Divine Confetti. Because you're crouching, you should have the chance to leap down and deliver a stealth blow to eliminate one of its health orbs. After you take it down, you'll be able to loot one of the Lapis Lazuli once you defeat it.
Pot Noble Koremori and The Giant Carp Quest
Likely by now, you've met this massive Carp who is swimming around the lake. As you progress and avoid this monstrosity, you're going to attend one of the Pot Nobles, who wish to become a carp. There was another, much earlier on in the game in Hirata Estate. There's an entire quest line devoted to these two, which we wrote up over here.
Before you do that quest, speak to the Pot Noble named Koremori, who is the one in the Fountainhead Palace. For six carp scales, you can purchase two Lapis Lazuli, and add them to your collection. Once you have bought them, you can continue to the Giant Carp quest and work towards changing them into a carp.
Once you've finished their quest, you'll have the opportunity to acquire more Lapis Lazuli by returning to the one who you turned into a carp. You're going to find it on the ground next to where they used to be.
The Demon of Hatred
Of all the ways to acquire Lapis Lazuli, you're going to find this the most difficult. After you defeat the Divine Dragon and obtain its tears, return to Ashina Castle. There, you're going to discover Lord Kuro has gone into hiding and Lord Issina has fallen to his sickness. Because he has died, his enemies are now invading the palace.
Now, instead of going down the main quest line path, you want to leave the palace and make your way to the Old Grave Sculptor's Idol. You should see a bridge in the distance that was not there before. Go that direction, and you'll find yourself in the Ashina Outskirts, where you're going to notice many familiar locations from the first part of the game. However, they're now on fire, and there are significantly stronger enemies roaming these areas. Continue until you make it to where the first mini-boss was, and you'll arrive at an idol that teleports you, instead of letting you rest. There, you'll find the Demon of Hatred wreaking havoc on anything in sight. Take it out, and you'll acquire two more Lapis Lazuli.
Those are all of the Lapis Lazuli you can find, and I'm sure if you've gone to upgrade your Prosthetic, you've noticed you cannot complete some of the final upgrades. It's because you need to continue a new game plus run of the game to acquire enough Lapis Lazuli to complete it properly.