I do see that your code is reading the potentiometer and stores the value in Delay (this would not be a great variable name as it can be confused with the delay function) ... should this be delayTime instead?

int t = analogRead(IN); //From the potentiometer

// Should this be "Delay" or "delayTime" ???
Delay = map(t, 0, 1024, 1, 1000); //we obtain the delay speed using the potentiometer
//we map the values from 1 to 1000 microseaconds

//MAIN CODE FOR LCD VOLTAGE DISPLAY
voltReading = analogRead(battPin);
volts = (voltReading / 1203) * 100;
if (volts == 100) {
  lcd.setCursor(12, 0);
  lcd.print(volts);
  lcd.print("%");
  delay(delayTime);
  lcd.clear();

  Serial.print(volts);
  Serial.print("%");
  delay(delayTime);
} else {
  lcd.setCursor(14, 0);
  lcd.print(volts);
  lcd.print("%");
  delay(delayTime);
  lcd.clear();

  Serial.print(volts);
  Serial.print("%");
  delay(delayTime);
}

#include <LiquidCrystal.h>

//BLDC CONTROLLER PIN DECLARATION
int AA1=3;
int AA2=5;
int BB1=11;
int BB2=10;
int CC1=9;
int CC2=6;

int enable=2; //This is not used for now, The ESC is always enabled
int emfA=A0;
int emfB=A1;
int emfC=A2;

int fase=1;
int deltaA=0;
int emA=0;
int sum=0;

int IN=A3; //pin A3
int Delay=4000;

int it=0;
int it2=1;

static int delta= 0;
static int Lastdelta= -1;

unsigned long previousMillis = 0;

//LCD PIN DECLARATION FOR BATTERY DISPLAY

LiquidCrystal lcd(13,12,8,7,4,1);

int battPin = A4;
int delayTime = 1000;
int voltReading;
int volts;

void setup() {
//SETUP CODE FOR BLDC CONTROLLER

Serial.begin(250000);
pinMode(AA1,OUTPUT);
pinMode(AA2,OUTPUT);
pinMode(BB1,OUTPUT);
pinMode(BB2,OUTPUT);
pinMode(CC1,OUTPUT);
pinMode(CC2,OUTPUT);

pinMode(enable,OUTPUT);

pinMode(IN,INPUT);
pinMode(emfA,INPUT);
pinMode(emfB,INPUT);
pinMode(emfC,INPUT);

digitalWrite(enable,HIGH);
previousMillis = micros();

//SETUP CODE FOR LCD VOLTAGE DISPLAY
lcd.begin(16,2);
pinMode(battPin, INPUT);
Serial.begin(9600);

}

void loop() {

//MAIN CODE FOR BLDC CONTROLER
int emA = analogRead(emfA);
int emB = analogRead(emfB);
int emC = analogRead(emfC);
int sum = (emA+emB+emC)/3;

unsigned long currentMillis = micros(); //count time


if(currentMillis - previousMillis >= Delay)
{

previousMillis += Delay;

//Phase1 C-B
switch(fase){
case 1:
digitalWrite(AA1,LOW);
digitalWrite(AA2,LOW);
digitalWrite(BB1,LOW);
digitalWrite(CC2,LOW);
digitalWrite(BB2,HIGH);
digitalWrite(CC1,HIGH);
delta = emA-sum;

break;

//Phase2 A-B
case 2:
digitalWrite(AA2,LOW);
digitalWrite(BB1,LOW);
digitalWrite(CC1,LOW);
digitalWrite(CC2,LOW);
digitalWrite(AA1,HIGH);
digitalWrite(BB2,HIGH);
delta = emC-sum;
break;

//Phase3 A-C
case 3:
digitalWrite(AA2,LOW);
digitalWrite(BB1,LOW);
digitalWrite(BB2,LOW);
digitalWrite(CC1,LOW);
digitalWrite(CC2,HIGH);
digitalWrite(AA1,HIGH);
delta = emB-sum;
break;

//Phase4 B-C
case 4:
digitalWrite(AA1,LOW);
digitalWrite(AA2,LOW);
digitalWrite(BB2,LOW);
digitalWrite(CC1,LOW);
digitalWrite(BB1,HIGH);
digitalWrite(CC2,HIGH);
delta = emA-sum;
break;

//Phase5 B-A
case 5:
digitalWrite(AA1,LOW);
digitalWrite(BB2,LOW);
digitalWrite(CC1,LOW);
digitalWrite(CC2,LOW);
digitalWrite(AA2,HIGH);
digitalWrite(BB1,HIGH);
delta = emC-sum;
break;

//Phase6 C-A
case 6:
digitalWrite(AA1,LOW);
digitalWrite(BB1,LOW);
digitalWrite(BB2,LOW);
digitalWrite(CC2,LOW);
digitalWrite(CC1,HIGH);
digitalWrite(AA2,HIGH);
delta = emB-sum;
break;
}

if (Lastdelta < 0){
if (delta > 0)
{
Lastdelta=delta; //save the last delta
fase= fase + 1;
if (fase > 6)
{
fase = 1;
}
}
}//Zero cross from - to +

if (Lastdelta > 0){
if (delta < 0)
{
Lastdelta=delta;
fase= fase + 1;
if (fase > 6) {
fase = 1;
}
}
}//Zero cross from + to -

}//Case ends

int t =analogRead(IN); //From the potentiometer
Delay=map(t,0,1024,1,1000); //we obtain the delay speed using the potentiometer
//we map the values from 1 to 1000 microseaconds

//MAIN CODE FOR LCD VOLTAGE DISPLAY
voltReading = analogRead(battPin);
volts = (voltReading/1203)*100;
if (volts == 100)
{
lcd.setCursor(12,0);
lcd.print(volts);
lcd.print("%");
delay(delayTime);
lcd.clear();

Serial.print(volts);
Serial.print("%");
delay(delayTime);
}
else
{
lcd.setCursor(14,0);
lcd.print(volts);
lcd.print("%");
delay(delayTime);
lcd.clear();

Serial.print(volts);
Serial.print("%");
delay(delayTime);
}

} //loop ends