Arduino Mega - Multithreaded (run two loops simultaneously) I am new to Arduino and I am not sure about how to get two loops run parallel to each other. I have tested the individual loops and both of them work perfectly before I combined them together. 

One loop will take input from the LCD touchscreen. One loop will take input from vibration sensor which will determine the state (on/off) of LED. Once the LED is turned on, it has to stay at the ON state for 3 seconds before switching to OFF state. 

The problem I am facing is that when the LED is triggered to ON state by vibration sensor, I have to wait 3 seconds for the input from LCD to get processed. Is there any way I can combine these two loops in such a fashion that I run them simultaneously, i.e. run two inputs together?
You can combine the 2 programs into 1 program.  But when you start wanting to do multiple things at once then you can't have any code that "blocks" and waits to finish before letting the next thing happen.  The Arduino has a single core, it can't do multithreading.  But if you write non-blocking code you can make things appear to happen at the same time.  I imagine the problem with your code now is that you have probably used the delay function.  That function blocks, so nothing else can happen while the delay is running.  Instead you have to use millis to record the time and periodically check against that time to see if it is time to take the next step instead of calling a delay to wait for the next step.  See the "Blink Without Delay" example that comes with the IDE and any of the multitude of tutorials about it on the web to see how it works.