How to find Lapp
For the first time you will meet Lapp after the opening of the new location "Garbage Pile". From the first bonfire, go down the hill and turn left into the ruins. Look at the rocks to the right and then fall into the library. Exit the library and turn right, skirting the wall past the first angel you see. Enter directly into the building and then through the door on the right. Now turn left, after which the tower will fall, creating a bridge inside the building. You will find Lapp by crossing the tower.
Then you need to find Lapp a second time. Head to the Earthen Peak Ruins bonfire and look for it nearby. He will tell you about a treasure in a nearby swamp. To find this treasure, head into the swamp, past the cottage, and into the cave under the massive roots. Stay close to the wall and follow the tunnel until it freezes over and you find a titanite slab. Now return to the fire and talk to Lapp again.
The third meeting takes place on the balcony by the Inner Wall of the City bonfire, which runs across the room from the gate leading to the elevator.
You will meet Lapp for the fourth time in the swamp. Stay close to the left wall until you spot a ladder. Climb the stairs and then head left into a circular room with several rings. Lapp is inside the room, sitting in a chair. After this meeting, you will be able to find the Purification Monolith, which will help Lapp remember who he is.
How to find the Purification Monolith
To find the Monolith of Purification, you will need to solve the puzzle "Show Your Humanity" Before you can solve this puzzle, you must first find it. Head towards the City Streets Beyond the Wall bonfire and then go through the metal gate between the two suits of armor. Look to your right to notice a broken statue on the ground. On the wall above the broken statue, there is a mysterious inscription that reads: "Show your humanity."
To complete the puzzle, return to the fire room and head through the door on the opposite side, the door that leads back to the swamp. Once here, use either the Young White Branch or the Chameleon spell. This will make you a Phantom. Now, being in your thin human form, return to the puzzle and a ladder will appear.
Climb the stairs to find yourself in a garden full of white flowers. Take a look around, pick up any good things you find, and then look around this area until you find a slightly rough-looking Purification Monolith. Now that you know where he is, it's time to find Lapp again and tell him about it. Return to the fourth location where you met Lapp.
Who is Lapp and how to get his armor
From here, continue the game until you reach the Shared Graf bonfire, where you first fight Darkeater Midir. Head over the nearby stone bridge, then follow the road on the right to reach the room where Lapp is sitting. He now knows his identity and rewards you by talking about a nearby treasure. Follow his directions and head to the edge of the broken staircase. A cutscene will start and Lapp will kick you out, revealing that he is actually Patch. He will leave his armor on the ground and disappear, so head back to where he kicked you out of to get Lapp's armor.
You can also just kill Lapp and then buy his armor from the Handmaiden in the Fire Temple.
