The Old Mine Lantern is in the Caverns, a region that opens in main quest chapter 4, DARK DESCENT. Stasis Transmutation is given as an altar reward about 90 m from the Lantern in a straight line. Other Caverns Lanterns close by are Mine Cart Route at about 190 m, Last Sunlight at about 260 m and Weeping Ledge at about 300 m.
The chests nearest the Lantern hold an Empty Ferrofluid Flask, a Ferrofluid Flask Power Upgrade, Pure Blade Material and Superior Firearm Parts, along with the Ambers Limit Break, Perfectionism and Surplus. The Mining Shaft Key and the Saltmine Note are also nearby. Lying near the Lantern are 5 Epic Catalyst Clots, 3 Legendary Catalyst Clots, 4 Nephtoglobin Vials, 3 Hand Grenades and 3 Standard Firearm Parts, plus 4 Special Ammunition, 4 Pistol Ammunition and 2 Stasis-Clad Rounds to restock your firearm.
Stasis Transmutation
Empty Ferrofluid Flask
Ferrofluid Flask Power Upgrade
Limit Break
Perfectionism
Pure Blade Material
Superior Firearm Parts
Surplus
Epic Catalyst Clot
Nephtoglobin Vial
Pistol Ammunition
Hand Grenade
Legendary Catalyst Clot
Standard Firearm Parts
Pistol Cartridges
Stasis-Clad Rounds
Crude Blade Material
Crude Transmutation Material
Deadly Rounds
Fire-Clad Rounds
Mining Shaft Key
Oil Grenade
Refreshing Vial
Remnant's Return
Stasis Whetstone
Whetstone
Mine Cart Route
Last Sunlight
Weeping Ledge