The String might have an extra space at the end; you can fix this by using String.trim():

1. if(isLukaszHome.trim().equals("0")){

Nope, no luck. Still not matching.

Do: println("isLukaszHome: "+ isLukaszHome.length());
to ensure your string is 1 char long.

I think PhiLho s right, there might be other characters inside the message. For example if i send an int-value from arduino, there are usually the ascii-characters 10 and 13 in the message (new line and line break).
I suppose, you could send the value as byte, since it is only 0 or 1.
But if its in a string, you could use indexOf() to check if the string contains a certain character. An example:

1. void serialEvent (Serial myPort) {
     String message = myPort.readStringUntil(13);
     if (message!=null) {
       print("message characters: ");
       for (int i = 0; i<message.length(); i++) {
         print((int)message.charAt(i)+ " ; ");
       }
       println();
   
       boolean isLukaszHome = false;
       if (message.indexOf('1') > -1)
         isLukaszHome = true;
       println("isLukaszHome: "+ isLukaszHome);
       if (!isLukaszHome) {
         //sendTweet("Lukasz left at: "+hour()+":"+minute());
         println("=> left");
       }
     }
   }
   

I also tried indexOf, and trim, neither seemed to work :(

You might try this, it tests the first character and sees if it is zero.
 
if(isLukaszHome.charAt(0) == '0')

nope. maybe there is something else in the code I am messing up and being stupid. Here is the entire thing:

I have only one more idea. Looking at the source code for the method readStringUntil it is possible for the method to return null and empty strings. Are you getting error messages for null reference exceptions?

Since the method can return null or empty string you should really test for these situations before attempting to use the string. This iseasily done by modifying the if statement e.g.

if( isLukaszHome != null && isLukaszHome.length() > 0 && isLukaszHome .charAt(0) == '0')

This will safely test the value returned by the readStringUntil method. The order of the boolean expressions inside the if statement must be as shown.

If you haven't been getting any error messages then this won't make any difference but is still worth a try.

If it doesn't work I don't have any more ideas.

nope, no errors. I am printing that variable and it seems to be ok, here is the output from debugger:

You have not answered my request...
I don't know how Arduino-Processing communication works exactly, but I find suspicious that you write an integer and expect a string at the other end... Unless Serial.write() automatically converts the int to a string, it cannot work.

Oops, sorry PhiLho! Slipped through the cracks. You are right, I think it is sending the entire string through even though its a new line, so It will never match. Using indexOf seems like it would work in this case but it throws an error saying "cannot convert from int to boolean" which is strange because I thought it was ASCII text...? Maybe this has to do with the serial connection it uses.

A byte is just a numerical value between 0 and 255 or, in the case of Java, between -128 and 127.
It is big enough to store an base Ascii char, like 'a' or '7' or '#'.

To send strings via serial connection in arduino you use "Serial.print()", for bytes you use "Serial.write()".
And i usually use "Serial.println()" to send a message, because its easy to sepreate messages if they have line-endings.
Because you are sending other information like "motion ended at " it could be a good idea to mark your messages with some kind of indicator that tells processing if the message is debug-information or a control-command.
For example "i" for info and "c" for control.
Then you could send messages like.

1. "i calibrating sensor"

1. "c 0"