Adjusting the light intensity with lcd.backlight () function

Other Hardware Displays
10

When you have a free PWM pin, you can use that pin to drive the backlight.
If you need to combine the LiquidCrystal_I2C with an "external" PWM pin, you could create your own class, inherit from the legacy class and add the needed functions to control the PWM pin.

something like that:

/*
  https://forum.arduino.cc/t/adjusting-the-light-intensity-with-lcd-backlight-function/1333947

  by noiasca
*/
#include <Wire.h>
#include <LiquidCrystal_I2C.h>

//create your own backlight enabled I2C class:
class MyLCD : public LiquidCrystal_I2C {
    const uint8_t blPin; //   UNO: 3, 5, 6, 9, 10, 11
  public :
    MyLCD (uint8_t lcd_Addr, uint8_t lcd_cols, uint8_t lcd_rows, uint8_t blPin) : LiquidCrystal_I2C(lcd_Addr, lcd_cols, lcd_rows), blPin(blPin) {}

    void init() {
      LiquidCrystal_I2C::init();
      pinMode(blPin, OUTPUT);
    }

    void backlight() {
      digitalWrite(blPin, HIGH);  // assumption HIGH active (on most PCF8574 a NPN transistor drives the LED cathode)
    }

    void noBacklight() {
      digitalWrite(blPin, LOW);
    }

    void setBacklight(byte val)  {
      analogWrite(blPin, val);
    }
};

//LiquidCrystal_I2C lcd(0x3F, 20, 4); // set the LCD address to 0x27 for a 16 chars and 2 line display

MyLCD lcd(0x3F, 20, 4, 9);  // address, columns, rows, PWM enabled backlight pin

constexpr uint16_t interval = 1500;

void setup() {
  Serial.begin(115200);
  lcd.init();                      // initialize the lcd
  lcd.backlight();
  lcd.setCursor(3, 0);
  lcd.print(F("Hello, world!"));
  lcd.setCursor(2, 1);
  lcd.print(F("backlight"));
}

void loop() {
  Serial.println(F("switch backlight off"));
  lcd.noBacklight();
  delay(interval);

  Serial.println(F("switch backlight on"));
  lcd.backlight();
  delay(interval);

  Serial.println(F("set backlight to 0"));
  lcd.setBacklight(0);
  delay(interval);

  Serial.println(F("set backlight to 64"));
  lcd.setBacklight(64);
  delay(interval);

  Serial.println(F("set backlight to 128"));
  lcd.setBacklight(128);
  delay(interval);

  Serial.println(F("set backlight to 192"));
  lcd.setBacklight(192);
  delay(interval);

  Serial.println(F("set backlight to 255"));
  lcd.setBacklight(255);
  delay(interval);

  Serial.println(F("set backlight to 0"));
  lcd.setBacklight(0);
  delay(interval);
}

You can disconnect the jumper and connect pin 1 to the PWM pin.
See also Dimming 16×2 and 20×4 LCD displays – Garry's blog