Using LCD Class Object as static member

Not 100% what you're trying to do with it, but this works:

I think I'm using a different LCD library to you so yours might need to be thumbed into this.

#include <LiquidCrystal_I2C.h>

class PCI {

  public:
  
    static PCI& Instance() {
      if (PCI::pInstance == nullptr) PCI::pInstance = new PCI();
    return *PCI::pInstance;
    }
    
    static LiquidCrystal_I2C lcd;
    
    static void test() { Serial.println("Serial Test"); }
  
  private:
    
    static PCI* pInstance; // Static variable holding the pointer to the only instance of this 
    
    PCI() {
      lcd.init();
      lcd.backlight();
    }
};
 
PCI* PCI::pInstance = nullptr;
LiquidCrystal_I2C PCI::lcd(0x27,16,2);

void setup() {
  Serial.begin(115200);
  PCI::test();
  PCI::Instance().lcd.print("LCD Test");
}

void loop() { }