I used the Non-Inverting with a LM358n ( so I could use the 0-5V as a source)
R1 9K (pot for fine tuning)
R2 1K
Total gain 10
Still used the 1.1 reference
I got the 10mV since the LCD only read 0.00 and I only see the last digit change. haven't figured out how to make the float display more digits yet. 
here is my code
// include the library code:
#include <LiquidCrystal.h>
// initialize the library with the numbers of the interface pins
LiquidCrystal lcd(12, 11, 5, 4, 3, 2);
//Variable to hold A0 reading 0-1023
int A0_Value=0;
float F1=0;
float PercentOfInput=0.0;
void setup() {
// set up the LCD's number of columns and rows:
lcd.begin(16, 2);
// Print a message to the LCD.
lcd.print("Hello, world!");
// Set Analog reference to Internal 1.1Volts
analogReference(INTERNAL);
}
void loop() {
// set the cursor to column 0, line 1
// (note: line 1 is the second row, since counting begins with 0):
lcd.setCursor(0, 1);
// print the number of seconds since reset:
lcd.print(millis()/1000);
// Set the curser to column 6 row 2
lcd.setCursor(6, 1);
lcd.print(" ");
lcd.setCursor(6, 1);
A0_Value = analogRead(A0); // read A0 value
PercentOfInput = float(A0_Value)/1023*100;
// lcd.print(A0_Value);
F1= (PercentOfInput)*0.011;
lcd.print(F1); // Print to LCD
lcd.setCursor(12,1);
lcd.print(A0_Value);
delay(500);
}/tt]