Unable to store data in variable from Serial.read()
You could try something like (not tested):    

void loop() {
 if(Serial.available()){
   input = Serial.parseInt();
   Serial.print("Data: ");
   Serial.println(input);
   if(input == 1){
      digitalWrite(RELAY, HIGH);
      digitalWrite(LED, HIGH);
   }
   else if(input == 2{
      digitalWrite(RELAY, LOW);
      digitalWrite(LED, LOW);
   }
 }
}


don't forget to declare input variable, use 1 to turn on, 2 off :)