PWM Control, How to stop LED from Flickering? What is required is controlling the brightness of an LED using both Buttons and a Potentiometer,
Button A: Increase

Button B: Decrease /Dim

Potentiometer: Increase and Decrease,

This however must happen on 1 single circuit and must display the results on an LCD.

If I do this separately, meaning buttons without potentiometer and visa versa, I win, the moment I combine the two. I get flickering when working the buttons, due to the potentiometer.

Alternative Research:https://www.instructables.com/id/Smooth-Potentiometer-Input/

Code Below

#include &lt;LiquidCrystal.h&gt;
#include &lt;Wire.h&gt;
// ------------------------------------------------------------

int LED1          = 9;
int ButtonLeft    = 8;
int ButtonRight   = 7;
int brightness    = 0;

// ------------------------------------------------------------
byte buttonState1     = 0;
byte lastButtonState1 = 0;

byte buttonState2     = 0;
byte lastButtonState2 = 0;

unsigned long switchMillis;

// ------------------------------------------------------------

int potValue1 = 0;
int potValue2 = 0;
int potPin= A0;
int readValue;
int writeValue;

LiquidCrystal lcd(12, 11, 5, 4, 3, 2);

// ------------------------------------------------------------
void setup() {

  lcd.begin(16, 2);
  pinMode (potPin, INPUT);
  pinMode(LED1,OUTPUT);
  pinMode(ButtonLeft,INPUT);
  pinMode(ButtonRight,  INPUT);
  lcd.clear ();
}

// ------------------------------------------------------------
void loop(){

    if (millis() - switchMillis &gt;= 5)
  {
    switchMillis = millis();
    checkSwitches();
  }

   readValue = analogRead(potPin);  
   writeValue = (255./1023.) * readValue;
   analogWrite(LED1, writeValue);

    potValue1 = analogRead(potPin) / 10;
    potValue2 = potValue1 / 1.02;

    lcd.setCursor(0,0);
    lcd.print("Potent=");
    lcd.print(potValue1);
    lcd.print("%");
    delay(100);
    lcd.print(" ");
    delay(1);
}

void checkSwitches() {

    analogWrite(LED1, brightness);
    delay(10); 

  buttonState1 = digitalRead(ButtonLeft);

  if(buttonState1 == HIGH){ 
    brightness--;
    if(brightness &lt; 0){
      brightness = 0;
    }
  }

  buttonState2 = digitalRead(ButtonRight);

  if(buttonState2 == HIGH){
    brightness++;
    if(brightness &gt; 255){
      brightness = 255;
    }
  }

 lcd.setCursor (0,1);
 lcd.print ("Brightness=");
 lcd.print (brightness);
 lcd.print ("   ");
}
Your code doesn't make much sense. 

You set the LED to 2 different brightness values that don't have anything to do with each other: The pot brightness and the button-based brightness. You only adjust the LED based on switches once every 5 mS. Thus the LED is going to flicker between 2 different brightness values.

What do you want it to do? How do you want to control the brightness based on input from both the pot and your switches? (What is the relationship between the buttons and the pot? Should the button input alter max/min value of the pot up and down? Should holding the button down change the brightness by 1 value per a specific time unit? Say 2 increments/decrements per second?)

Describe the user interface you want to achieve, and then think through how you would do that in code.