I believe LRC throws away the econ cruise index no which allows the FMC to work out the best speed for fuel cost v aircraft cost and gives best fuel economy.
The assumed temperature method is where the man gets.....oops
I'll start again
The assumed temperature method is where the engines are derated to an asssumed temperature where they produce they produce sufficient thrust to satisfy performance requirements for the prevailing WAT conditions. This saves engine life and builds in extra performance insofar as the air is denser than assumed and therefore the aircraft will perform in excess of that temperature.