I will try BG 44K should I have this type of problem with my LS460. I previously had a very well cared for LS430 and at about 150K is started really bogging/hesitating during acceleration seemingly out of nowhere. I hooked up my OBD2 reader and didn't find any codes. I felt strongly that there wasn't anything seriously wrong with the engine/intake/fuel system and I wasn't confident my mechanic would be able to isolate the problem without some trial and error costing me $$$. I did a bunch of research and ended up buying MAF sensor cleaner at the auto parts store. After removing and cleaning the MAF sensor, I noticed a positive difference but it didn't resolve the issue completely. I then bought a new OEM (Denso) MAF sensor (about $80 on Amazon) and the car ran like new again. Never had any more problems and eventually sold the car almost three years later.
LS460s have dual air intakes, two MAF sensors, two air filters, etc. so it would make sense to use the BG 44K before replacing MAF sensors. If the fuel system cleaner doesn't work, the mass air flow sensors are another possibility. They should last a very long time but they don't last forever. They are extremely sensitive and should be cleaned and/or replaced on a high mileage car when having this type of problem before digging too much deeper.