Diodes and LEDs are thermometers. Do you want the voltage to change when the temperature changes or as they warm up?
Transistors too. An IC voltage reference or regulator is designed to have no thermal problems.
It will be very hard to find opamp working with 1.5V supply.
If You really need LDO working with 1.5V supply with 1.35V of output, You should use bandgap reference (~1.25V) and make an error amp on emitter degenerated NPN BJTs
If a proper transistor is biased and placed in series, its VCE(sat) will already be 0.1-0.25 V,I think it's enough ..
2 Resistors and 1 silicon transistor..
The reference is an led and diode stacked inline. The diode is added to raise the reference by 0.6V. This is needed because 0.6V is dropped across the bias-emitter junction.