Well, ignoring the fact that you seem to think offensive items are the only items that exist (completely ignoring defensive and utility items which are core for many champions) and the fact that base damages exist:
Annie stacks AP and Magic Pen.
Darius's core item is Black Cleaver (and he typically gets another AD item at some point).
Elise builds Runic Echoes and Rylai's Crystal Scepter (occasionally Abyssal Scepter, Liandry's Torment, and/or Void Staff)
Fiora requires at least two AD items (typically Hydra and Black Cleaver, maybe Maw of Malmortius too)
Gragas builds Runic Echoes into Iceborn Gauntlet.
Graves build AD/AtkSpd/Crit/ArmorPen in every role he fills.
Kindred typically gets Warrior or Devourer into Runaan's Hurricane and/or BoRK, at minimum.
Leblanc stacks AP and Magic Pen.
Lee Sin builds Warrior and typically gets at least one more AD item (i.e. Black Cleaver or Maw of Malmortius).
Nidalee builds Runic Echoes into Rod of Ages, stacking AP and Magic Pen.
Pantheon stacks AD and Armor Penetration (typically Youmuu's Ghostblade into Black Cleaver and Maw of Malmortius).
Renekton builds Black Cleaver and Hydra or Maw of Malmortius.
Zed is an AD assassin who stacks AD, armor pen and CDR.