LCD Shield and Arduino
Note: While looking at specifications can infer compatibility, there is no substitute for prototyping.  It is always better to try something then ask for suggestions if it does not work as expected.

That said, I would suggest to look at the LCD you specified.  The LCD's physical shape appears to lock you into a legacy Arduino Uno layout.

On the LCD's web page is a list of pins used.

On the HX711 sparkfun.com web page is a diagram of pins used when using their HX711 software.

Check if there are any conflicts.  Even if there are none, it does not mean there will be no conflicts within the software you will need to run the LCD and the HX711.  You will have to either find someone who has successfully done exactly what you want to do or examine all the software involved your self.  Of course you could simply prototype the project to see if it works.