My understanding is that it's an airframe/engine balance. Ideally we'd like to keep the aircraft flying at close to optimum angle of attack (best lift to drag) with the engines operating close to their optimum design rpm (best sfc). For a given altitude as weight decreases and thus also required lift, keeping angle of attack constant we would need to slow down and thus have the engines operating slower than optimum, and not as efficiently. By climbing into thinner air the aircraft has to travel faster for the given angle of attack and also the engines have to operate closer to their design speed thus given better track miles for the fuel burnt.
almost.
It's TAS/drag not lift. If we use lift then we are flying for endurance not range.
SAR=(1/SFC)(TAS/Drag)
see my previous post for a full explanation.