Why does the LCD impede the ESP8266 NodeMCU initialization?
Certains pins of the ESP are boot mode selection straps, and are internally weakly pulled high or low to boot normally, but these can be overridden externally to select other boot modes (to load firmware etc).
The LCD data, R/W and RS pins all have internal weak pull-ups to LCD supply voltage. These weak pull-ups of the LCD module override the weak pull-downs of the ESP, and select a boot mode where it does not boot normally.
What is even worse, is that the ESP pins are rated for 3.3V IO voltages, and the LCD pull-ups try to pull them to 5V. The current is very small due to the pull-up resistances are generally quite high, but still this should not be done for long-term reliability.