How to turn off and turn on LCD 16*2 display?
When you disconnect to turn off and then reconnect to turn on your LCD without restarting your device (if you unplug and re-plug it for instance) the initialization procedure is not executed and your LCD will not be correctly configured.
If you want to turn off the LCD and then on in the middle of operations use the instruction register allowing to turn it on or off by software:

Your LCD may have different configuration but it must be similar check its datasheet.
If you are using LiquidCrystal_I2C library on Arduino use noDisplay() and display() functions.
These functions use the flag LCD_DISPLAYON that has the value 0x04 to point to the bit D shown on my figure (LCD_DISPLAYOFF set to zero to turn it OFF).
If you want to reduce consumption (which I think is your goal) read @SpehroPefhany comment that insists on turning off the backlight.