Punching in some quick numbers:
NRT-HKG is about 1650nm. For a cruise segment of say 1500nm.
1. At FL370, you burn16850kgs of fuel,
2. At FL240 you burn 15460kgs of fuel.
So simplistically, for fuel alone, it is better to fly lower in this case. The will be time related savings as well due to shorter flight time at the lower level. As I say it is simplistic, in that extra fuel will be used to climb to 370, but less fuel used in the (longer) descent.