Delta-V to Mars via EML-2 vs. Delta-V to Mars via LEO

It isn't that much difference in terms of Delta V from going from LEO - EML-2 than for  LEO-MTO ( Mars Transfer Orbit.)  It's about 1 kilometer /sec difference in velocity.

Both ways require pretty much the same maneuvers from where they are to where they are going.  There may be an advantage for EML-2 in that it may be easier to -obtain water and oxygen from the moon- than from LEO.  From there, EML-2 can be used as a staging point to go to Mars.

LEO can be used for staging for Mars as well, if that is desired.  However, when staging at LEO, any additional supplies have to come out of a deeper gravity well.  That means bigger and more expensive rocket, or more rocket launches, or both.

The mass fraction for the moon is about 1/2.  The mass fraction from Earth is maybe 2% to get to lunar orbit from LEO, and a lot less than that to go all the way to Mars.  You can put the more cargo at EML-2 than in LLO ( lower lunar orbit).  However, the downside is the need for infrastructure on the moon in order to obtain the water, oxygen, and perhaps other supplies.

Putting it another way, there is no disadvantage in terms of Delta-V worth mentioning to stage from EML-2.

You have the additional opportunity to supply your ship for the long voyage to Mars without having to launch it all from Earth at one time.

Musk may be planning to use the Martian atmosphere for aerodynamic braking.  This will require less fuel provided that the heat shield isn't too heavy.

Numbers obtained here.