They will remain beyond my grasp if you don't express them. The O.P. was not your view because you immediately amended it in post #3.
I don't think Lewis is necessarily the best advocate for your beliefs. He was a High Church Anglican and certainly no sort of evangelical. However, what does it mean that the Lord Jesus died on our behalf?
If I write a letter on your behalf, I write it and you don't. I write it instead of you.
If you win the Congressional Medal of Honour (how long can it be?), but are unable to go to receive it, I might do so on your behalf; I collect it instead of you.
In both of these examples, I am doing something for your benefit.
If you have tickets to a big baseball match and I steal them from you, I would go to the match instead of you, but I wouldn't be going on your behalf. I am not doing something for your benefit.
So to do something on someone's behalf means to do it instead of him, but for his benefit. Christ gave His flesh for our flesh; He suffered in the flesh instead of us, so that we don't have to. He gave His life for our life; He died that we might live forever. He did both those things for our benefit, so they are on our behalf.
What you (and Lewis) are arguing is that Christ died for our benefit, but not instead of us. But what you cannot deny is that He suffered and we don't. What benefit is it if Christ dies and it is not in our place? Where is the justice of God in that?