Which LCD Pins, if any, require PWM?
Likely all programmable pins on modern embedded processors are able to perform digital I/O.  In addition, many can also perform other tasks such as PWM, or Analog to Digital Conversion (ADC).  This is true for many of the different processors used on different Arduino boards.

Often, the nice people who write the C++ driver class of programs or Arduino Libraries offer the user the ability to change pin assignments used by the Arduino Libraries when instantiating an instance of the driver.  This is true for the LiquidCrystal driver in the tutorial in the question.  This can be an advantage as processor's resources are limited.  For example, if you need PWM controlled pin to dim LEDs, you can move LCD controlling pins to other non-PWM pins.

The LCD specified in the tutorial linked to in the above question uses a common Hitachi HD44780 interface.  Such assemblies only need embedded processor Digital I/O pins for control.  Had the LCD no electronic driver, the segments need to be directly driven by very low alternating current (AC).  This is difficult for embedded processors.  However, it may be possible using enough PWM pins and some clever software &amp; hardware.