ADC not working

Not sure if this is the cause, but

  int x_ax = analogRead(0);

  if(x_ax <= 504) {lcd.print("R");}
  if(x_ax == 507) {lcd.print("N");}
  if(x_ax >= 510) {lcd.print("F");}

Your code above won't print anything if analogRead(0) returns one of these values: 505, 506, 508, 509.

  int x_ax = analogRead(0);

  if (x_ax <= 504) {lcd.print("R");}
  else if (x_ax >= 510) {lcd.print("F");}
  else { lcd.print("N");}

This prints "N" for any value in the neutral dead-band between your "R" reverse and "F" forward thresholds.