Kill the Orc Captain and present his belt to Mathew the dwarf.
Just inside the doors of Erebor another key can be found by the door, you merely need to take this one (although you have to be inside the locked doors first.)
You can get a A whole-roasted rabbit.
get rabbit
After killing the An Orc captain is here and looting a swordbelt.
do sw,e,3ne,2e,2d,n,2u,climb rope,give belt to dwarf
He will give you the key to the doors of Erebor.
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