The low-pressure cutoff is managed by a pressure sensor (often called a low pressure switch, although it's more accurately a pressure sensor) that's part of the AC system. This sensor *sends a signal* to the compressor clutch's control circuit, causing the clutch to disengage if the pressure drops too low. This protects the compressor from damage. The location of this pressure sensor varies slightly by year and model, but it's typically near the evaporator or accumulator (often a dryer). You'll likely find it on a low refrigerant line. Look for a small electrical connector on a line near these components.
To find this sensor, you'll likely need a shop manual specific to your 1997 Chevy Lumina 3.1L. A wiring diagram will be helpful to trace the circuit to confirm its location and role in the system.