@golaat My setup is exactly that. I installed (soldered) a barrel connector on the PowerBlock and use a barrel-type power supply (5V, 4A) which provides power to the Pi via the GPIO pins. I do not have to use the micro-USB connector to power the Pi. The Pi will draw whatever it needs from the power supply and whatever USB device that is connected to it that requires power. I do not experience any power shortage at all. The Pi does not overheat either and I do not have to use a fan, but if it does I have enough power for the fan as well.
If you use the same type of setup and power supply unit as mine, you will not need the extra power supply and relay board to power the LCD. The PowerBlock has solder holes for 5V_OUT to connect to external devices such as in your case a 5V LCD. The 5V_OUT is also controlled by the switch on the PowerBlock.