Start by speaking to Sigmund on the first floor (second floor US), and he will explain that a wall has collapsed in the cellar. He asks you to talk to people around Lumbridge to see if they saw anything.
Try speaking to any of the people mentioned below. One of them (differs per person) will explain they saw a goblin in the cellar.
- Duke Horacio
- Father Aereck
- Any of the men or women in Lumbridge
After finding out who said they saw the goblin, return to the Duke and you will talk him into investigating. Look for the rubble on the wall in the southeast corner of the cellar, and mine it.
Head through (with a light source!) and pick up the brooch on the ground. Return to the duke and show him. Sigmund will have a fit and suggest wiping out the goblins. The duke asks you to do research on the brooch before going any further.
Head to the Varrock Palace Library and speak with Reldo. Search the northern most bookcase on the western wall. Compare the symbols in the book with the brooch to find that it belongs to the Dorgeshuun goblins.
Next head to the Goblin Village north of Falador. Speak to Generals Wartface and Bentnoze. Use the following options.
- Have you ever heard of the Dorgeshuun?
- It doesn't really matter
- Well either way they refused to fight
- Well I found a brooch underground...
- Well why not show me both greetings?
They will then show you both emotes.
Return to the Lumbridge cellar and enter the cave. Take the following path to avoid traps.
Look nearby for Mistag. Use the Goblin Bow next to him, and he will talk with you. He will explain that the break-in to the cellar was an accident. He asks to make peace. After talking with him, you can right click follow him to the start of the maze.
Return to the duke, and you will try to explain, but you will be informed that some silverware is missing from the cellar. Pickpocket Sigmund, then open the chest in the room to the south. You will find some Humans Against Monsters robes. Head west from Lumbridge to a ruined building.
In the northwest corner, right click and picklock the trapdoor. When it's opened, climb down and search the nearby crate to find the silverware. Return to the duke, and he will oust Sigmund.
The duke will give you a treaty and asks that you take it to the cave goblins. At the start of the maze, you will now find Kazgar. Right click to follow him to the mines. Speak to Mistag and show him the peace treaty. He will summon Ur-tag, the goblin leader, to sign it.