Serial Monitor

I have successfully learnt how to print characters on LCD display using HC-05. As I am using Serial Monitor, I need the Arduino UNO to be connected to PC or laptop for this project. But I want to if I can use it only with the power supply and without laptop or PC.

Sure,the serial port & functions are only there when you need them.
Write to the KCD in the same way, ignore the Serial.prints.

(Better still, Remove all references to serial if your code isn’t dependent - as it will run slightly faster... the serial pipe adds a tiny amount of time to pump out the characters (or waiting for inout)).