I read them all and that's where the confusion comes from.
You talk about a crashing ESP01, with the LCD connected to the Arduino. Now when we ask for the offending code you only provide partial code, claiming it runs on the ESP01 but it has LCD code in it, while you say the LCD is not connected to the ESP01 but to the Arduino!
Maybe the problem is indeed in the connections, hope you can get it work. But I also hope you understand the confusion you cause by posting contradicting information (and of course incomplete code is useless), and that this wastes our time.