What i'm getting from that is that you have a MEGA2560 and a plug in shield called RAMPS1.6 (some sort of motor controller?).
You also have an LCD shield that integrates an LCD, touchscreen and SD card reader.
Given that the MEGA2560 will be on the bottom of the board stack and the LCD on the top of the board stack ( 
), that means that your controller board will be in the middle.
Does the controller board support another shield stacked on top of it?
What about cooling requirements, assuming that your controller board gets hot...
What signals does each board need from the MEGA2560?
Post some links to what you've bought.