My first post as a "hope-to-be-soon-owner" of an LS400.
A faulty thermostat that hangs open will cause two problems. 1, it keeps the ECU in warm up mode which is richer than it needs to be. 2, the engine will not burn the fuel as efficiently and will require more throttle input thusly more consumption.
A K&N will only flow better if the paper filter it is replacing is too small or causes some restriction. This is usually more noticable at higher rpm/throttle openings unless the factory paper filter is large enough to accomodate the engine to begin with. A K&N will flow better per square inch than paper.
Has anyone tried running 89 or 87 octane? If this engine has a knock sensor it should be able to compensate. Premium "Pump" gas is the least thermally efficient fuel you can run. I'd guess that the combustion chamber and compression ratio of the LS is not prone to detonation, the only reason to run higher octane. Premium "pump" gas kills perfomance and efficiency in the process of preventing knock/detonation.
Is there a taller rear gear available? A friggin' Corvette gets mid to low 30mpg highway due to its tall final gearing. 350 to 420 horsepower/torque with no regard for economy. Sure it only weighs around 3,000 lbs but it also only turns in the 1,700rpm range at a 75mph cruise in top gear. What does an LS turn at 75mph?