The behavior of my null indicator changes based on
a) the opamp is rail2rail or not,
b) the opamp can work at +/- 2.5V
c) the LED diode forward voltage - with only +/- 2.5V your LED's Vf has to fit somehow (based on the color the Vf is from 1.6V to 3.5V, afaik).
PS: I doubt your above indicator may work as there is none feedback manipulating the input threshold levels..
PPS: Recommended reading:
Jerald G. Graeme: Applications of Operational Amplifiers, Third-Generation Techniques, McGraw-Hill, 1973, p.112