Hello,
You will need to operate the 'QE32 device from a 3.3 volt supply, and the LCD display from 5.0 volts. However, assuming that the HD44780 is permanently set to write mode (as is often the case), the 3.3 volt swing from the MCU output pins should still be compatible with the switching threshold of the data and control inputs to the display. Check this is true for the display you are using.
Regards,
Mac