An altar about 20 m from the Main Hall Lantern in a straight line gives you Shield Transmutation as its reward. Main Hall sits in the University, a region that opens in main quest chapter 9, IN RUINS. The closest other Lanterns of the University are Sewage Drain at about 90 m, Laboratories at about 130 m and Lift Shaft at about 170 m.
The chests nearest Main Hall hold 2 Distilled Blade Material, an Empty Ferrofluid Flask and a Quintessential Transmutation Material. Look for the Auditorium Key and the Library Key nearby. Items lying close to the Lantern are 3 Nephtoglobin Vials, 2 Stasis-Clad Rounds, 2 Mighty Rounds, an Imperial Catalyst Clot, a Mythic Catalyst Clot, an Eternal Catalyst Clot, a Stasis Whetstone and Pistol Ammunition. The Orphan is the boss fought near Main Hall, which makes this Lantern a place to rest and level up before that fight.
Distilled Blade Material
Empty Ferrofluid Flask
Quintessential Transmutation Material
Nephtoglobin Vial
Mighty Rounds
Stasis-Clad Rounds
Auditorium Key
Crude Transmutation Material
Distilled Transmutation Material
Eternal Catalyst Clot
Exquisite Firearm Parts
Fire-Clad Rounds
Hand Grenade
Imperial Catalyst Clot
Library Key
Mythic Catalyst Clot
Pistol Ammunition
Sands of Time
Stasis Whetstone
Sewage Drain
Laboratories
Lift Shaft