Simple Solution

#include <Adafruit_Sensor.h>
#include <DHT.h>
#include <DHT_U.h>
#include <LiquidCrystal.h>
#include <Servo.h>

#define PIR_PIN 4
#define DHTPIN 1
#define DHTTYPE DHT22
DHT_Unified dht(DHTPIN, DHTTYPE);

#define FAN_PIN 10
#define LED_PIN 11
#define SERVO_PIN 9

LiquidCrystal lcd(12, 13, 4, 5, 6, 7);
Servo door;

void setup() {
  pinMode(DHTPIN, INPUT);
  pinMode(PIR_PIN, INPUT);
  pinMode(FAN_PIN, OUTPUT);
  pinMode(LED_PIN, OUTPUT);

  analogWrite(FAN_PIN, 0);
  analogWrite(LED_PIN, 0);

  dht.begin();
  lcd.begin(16, 2);

  door.attach(SERVO_PIN);
  closeDoor();

  attachInterrupt(digitalPinToInterrupt(PIR_PIN), openDoor, RISING);
  attachInterrupt(digitalPinToInterrupt(PIR_PIN), closeDoor, FALLING);
}

void loop() {
  maintainTemp();
  delay(5000);
}

void maintainTemp() {
  float temperature = getTemp();
  int humidity = getHumidity();
  printToLcd(temperature, humidity);
  float temp = constrain(temperature - 5, -3, 3);
  int analog = map(abs(temp), 0, 3, 0, 255);
  if (temp > 0) {
      analogWrite(FAN_PIN, analog);
      analogWrite(LED_PIN, 0);
  } else {
      analogWrite(FAN_PIN, 0);
      analogWrite(LED_PIN, analog);
  }
}

float getTemp()
{
  sensors_event_t event;
  dht.temperature().getEvent(&event);
  if (isnan(event.temperature)) {
    return 0;
  }
  else {
    return event.temperature;
  }
}

int getHumidity()
{
  sensors_event_t event;
  dht.humidity().getEvent(&event);
  if (isnan(event.relative_humidity)) {
    return 0;
  }
  else {
    return event.relative_humidity;
  }
}

void printToLcd(float temp, int hmd) {
  lcd.clear();
  String tempData = "Temp: " + String(temp);
  lcd.print(tempData);
  lcd.setCursor(0, 1);
  String tempHmd = "Humd: " + String(hmd) + "%";
  lcd.print(tempHmd);
}

void openDoor() {
  door.write(110);
}

void closeDoor() {
  door.write(70);
}