Why Lelouch needs geass in his two eyes?
I have a theory about this.

The Geass consists in three stages: 
Normal stage -> Lost control stage -> Both eyes stage.

The point with third stage is that, only in this stage, the user is able to complete his/her contract and become a Code. Lelouch and any other Geass' users will not show any difference in his/her power level or new abilities, since this stage only remarks the new capacity of the user to become a Code.

After watch the anime twice (and Akito once) I think this makes sense and there is not (as far as I remember) anything that contradicts it.