Please explain to me how this N1 with more fuel, and FAR MORE (4X!!!!) LIFT/ACCELERATION at Launch - had a smaller lunar payload capacity?
OK, here are some numbers for you, which took me all of two minutes to dredge up. The first stages of the Saturn V and the N1 (the ones that actually generate that liftoff thrust) compare thus:
Saturn V S-IC stage dry mass: 303,000lb
N1 block A dry mass: 423,000lb
Saturn V S-IC propellant mass: 4,578,000lb
N1 block A propellant mass: 3,858,000lb
Saturn V S-IC burn duration: 263 seconds
N1 block A burn duration: 113 seconds
So the N1 burns through less fuel in less than half the time in its first stage flight, accelerating a heavier dry mass and heavier upper stages. It then continues using the same kerosene/LOX combination in all the other stages, while the Saturn V upper stages used the more efficient liquid hydrogen/LOX combination*. Additionally the design of the N1 was staggeringly inefficient, with a conical outer wall containing spherical fuel tanks. The Saturn V fuel tanks were the body of the rocket (and the upper stages did away with any intertank void such as those between the fuel and LOX tanks in the first stage by using a common bulkhead to separate fuel and LOX), and so a greater proportion of the fully fuelled mass was fuel compared to the N1.
*The difference in mass between liquid hydrogen and kerosene is something you have also failed to take into account when simply declaring the N1 had 'more fuel'. It may have had more fuel by mass but that's not a good comparison.