Methane/lox engine to gather hydrogen from Moon for Mars trip

quick and dirty speculative post about how to get to Mars with the least amount of help from Earth:

What about that idea of using a methane/lox engine to shuttle an empty tank from L2 down the surface, and bring back hydrogen for an NTR engine?

For every 100k pounds of wet mass to Mars, you need about 20k pounds of hydrogen for the trip.  The goal is to get that 20k pounds from the Moon using Methane delivered from the Earth.  Eventually, you'll be making methane, and you won't even need fuel from Earth at all.

For every 20k pounds of cargo from the surface of the moon, you need 44% of the wet mass to get it to EML-2 when using a methane lox engine.

Lets say the hydrogen tank weighs 10k pounds.  That's 30k that has to go the surface.  Add another 10k for the engine and return oxygen and methane.  ( that might be wrong )  So, you need probably around 30k for the fuel to get to the surface.  You are bringing back 50k, so you need about 50k fuel from the surface.  Eighty percent of that is oxygen from the moon.  So, that leaves 10k for the methane.  The numbers will have to be adjusted because that is too much fuel being used.

Or use a smaller tank and more trips.

Let's say 4 trips to get all of our hydrogen.  That's 5k on each trip.  Let's say the tank weighs 3k.  That's 8k that has to go back up.  Double that for the methane/lox engines and such.  That's 16 k for the trip up, so you need 16 k ( or less since it is 44%)  fuel for the trip up.  An empty tank releases 5k for the trip down.  The trip up requires 3.2k of methane, leaving some balance for the trip down.  The trip down need 11k for fuel, of which 2.2k is methane.  So, you are using about 5.4k lbs of methane to deliver 5k pounds of hydrogen.  But the 5k pounds of hydrogen in the NTR goes twice as much in delta v, so its like doubling your propulsion capacity.

I'm guessing that it is worth doing.

Loxleo could supply oxygen for the trip down, a lunar base could supply oxygen and hydrogen for the trip back up with the hydrogen for the trip to Mars.