Example of using an Arduino with Ethernet shield to control Philips Hue, with PIR motion sensor on i/o pin 2.

Control Philips Hue from Arduino Ethernet Shield

/*
    Talking to Hue from an Arduino
    By James Bruce (MakeUseOf.com)
    Adapted from code by Gilson Oguime. https://github.com/oguime/Hue_W5100_HT6P20B/blob/master/Hue_W5100_HT6P20B.ino
    
*/
#include <SPI.h>
#include <Ethernet.h>
 
//  Hue constants
 
const char hueHubIP[] = "192.168.1.216";  // Hue hub IP
const char hueUsername[] = "newdeveloper";  // Hue username
const int hueHubPort = 80;

// PIR
int pir = 2;
boolean activated = false;

//  Hue variables
boolean hueOn;  // on/off
int hueBri;  // brightness value
long hueHue;  // hue value
String hueCmd;  // Hue command

unsigned long buffer=0;  //buffer for received data storage
unsigned long addr;
 
//  Ethernet
 
byte mac[] = { 0x74,0x69,0x69,0x2D,0x30,0x31 };  // W5100 MAC address
IPAddress ip(192,168,1,2);  // Arduino IP
EthernetClient client;
/*
 
    Setup
 
*/
void setup()
{
  Serial.begin(9600);
  Ethernet.begin(mac,ip);

  pinMode(pir,INPUT);
  delay(2000);
  Serial.println("Ready.");
}

void loop() 
{
  if(digitalRead(pir) == 1){
    Serial.println("activated");
    
     // A series of four sample commands, which colour fades two lights between red and pink. Read up on the Hue API
    // documentation for more details on the exact commands to be used, but note that quote marks must be escaped.
    String command = "{\"on\": true,\"hue\": 50100,\"sat\":255,\"bri\":255,\"transitiontime\":"+String(random(15,25))+"}";
    setHue(1,command);
    command = "{\"on\": true,\"hue\": 65280,\"sat\":255,\"bri\":255,\"transitiontime\":"+String(random(15,25))+"}"; 
    setHue(2,command);
    command = "{\"hue\": 65280,\"sat\":255,\"bri\":255,\"transitiontime\":"+String(random(15,25))+"}";
    setHue(1,command);
    command = "{\"hue\": 50100,\"sat\":255,\"bri\":255,\"transitiontime\":"+String(random(15,25))+"}"; 
    setHue(2,command);
    
    // so we can track state
    activated = true;
  }
  else{
    
      activated = false;
      Serial.println("deactivated");
      
      //was activated, so send a single off command
      String command = "{\"on\": false}";
      setHue(1,command);
      setHue(2,command);
     
  }
  
}

/* setHue() is our main command function, which needs to be passed a light number and a 
 * properly formatted command string in JSON format (basically a Javascript style array of variables
 * and values. It then makes a simple HTTP PUT request to the Bridge at the IP specified at the start.
 */
boolean setHue(int lightNum,String command)
{
  if (client.connect(hueHubIP, hueHubPort))
  {
    while (client.connected())
    {
      client.print("PUT /api/");
      client.print(hueUsername);
      client.print("/lights/");
      client.print(lightNum);  // hueLight zero based, add 1
      client.println("/state HTTP/1.1");
      client.println("keep-alive");
      client.print("Host: ");
      client.println(hueHubIP);
      client.print("Content-Length: ");
      client.println(command.length());
      client.println("Content-Type: text/plain;charset=UTF-8");
      client.println();  // blank line before body
      client.println(command);  // Hue command
    }
    client.stop();
    return true;  // command executed
  }
  else
    return false;  // command failed
}

/* A helper function in case your logic depends on the current state of the light. 
 * This sets a number of global variables which you can check to find out if a light is currently on or not
 * and the hue etc. Not needed just to send out commands
 */
boolean getHue(int lightNum)
{
  if (client.connect(hueHubIP, hueHubPort))
  {
    client.print("GET /api/");
    client.print(hueUsername);
    client.print("/lights/");
    client.print(lightNum);  
    client.println(" HTTP/1.1");
    client.print("Host: ");
    client.println(hueHubIP);
    client.println("Content-type: application/json");
    client.println("keep-alive");
    client.println();
    while (client.connected())
    {
      if (client.available())
      {
        client.findUntil("\"on\":", "\0");
        hueOn = (client.readStringUntil(',') == "true");  // if light is on, set variable to true
 
        client.findUntil("\"bri\":", "\0");
        hueBri = client.readStringUntil(',').toInt();  // set variable to brightness value
 
        client.findUntil("\"hue\":", "\0");
        hueHue = client.readStringUntil(',').toInt();  // set variable to hue value
        
        break;  // not capturing other light attributes yet
      }
    }
    client.stop();
    return true;  // captured on,bri,hue
  }
  else
    return false;  // error reading on,bri,hue
}

The reason your code takes so long to run and update the change of input is because of the while loop on line 90. You don't need that while loop. You should also only be calling setHue when the switch input changes from off to on, or on to off. Your current code continuously calls upon setHue even if the state is the same.
I suggest changing line 51 to:
if((digitalRead(pir) == 1) && (activated == false) ){
and line 68 to:
if((digitalRead(pir) == 0) && (activated == true) ){