I bet the problem is in the code you tried, but didn't bother to include with your post. Did you start with just ONE device and learn how to program for it? Do you have a program that makes the servo work the way you want it to work? Do you have a program that makes the IR proximity sensor work the way you want it to work?
Once you get the individual parts figured out, then write a program to use your two sensors to do what you want. And when that runs ok, add the LCD code and get it to work. By then you will know where to place code to operate the servo.
DO NOT try to do it all at once!!!
Paul