All of your code is in setup(). The setup() function runs once and then program control goes to loop(). So if you are not holding the button down during start up it will not be read as HIGH. And "Jon" is printed whether or not the button is pushed. There are other things wrong with the code such as the lcd constructor is called in setup() so the lcd will not exist anywhere else (see scope). Make the lcd constructor global. And you only need one lcd.begin statement. Also pin 2 is used for both the button and the LCD. That won't work.
Have you read the pages that I linked in reply#1? Will you answer all of the questions that I asked? Does the button switch have a pull down resistor?
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I believe that you would benefit by reading some basic Arduino coding tutorials.
Basic Arduino programming.
Basic C++ tutorial