I've heard an argument that moon landing was at best improbable as it would have required too much more fuel than simply achieving LEO. It seems to me that it would be relatively little more. I'm just looking for a percentage of fuel burned after clearing the atmosphere by a craft headed for the Lagrange point.
To further simplify the problem, we can assume that the launch is straight up, the Moon is stationary with respect to the launch point and the final velocity upon reaching the Lagrange point is 0.
For practical purposes, I think fuel weight would have to be included in the ratio, but that stage separation can be neglected as it tremendously complicates things and the entire launch mass, minus all fuel, reaches the Lagrange point.
Bonus: To what degree does it matter whether the moon is new or full?