The zones of House of Thule are broken down into tiers:

Tier 1

Feerrott and House of Thule (lower) - Gear is attuneable, Req 80, Rec 85

Tier 2

The Grounds, The Well, The Library, and Erudin Burning - Gear is No Drop, Req 82, Rec 87

Tier 3 (locked)

House of Thule (upper), Al'Kabor's Nightmare, Miragul's Nightmare, and Fear Itself - Gear is No Drop, Req 85, Rec 90

Tier 4

Morell's Castle and Sanctum Somnium - Gear is No Drop, Req 90