Moral argument has 2 unfounded premises.

The moral argument for god as i understand it is:

Major premise - All laws have a lawmaker.

Minor premise - There is a moral law.

Conclusion - Therefore, there is a moral lawmaker.

The logic here is irrefuteable however i can challenge both premises.

All laws have a lawmaker

This is false. I can demonstrate this with the law of identities. Something is itself. or A = A
This law could not have a lawmaker because prior to its creation the creator wouldn't be itself and something that isn't the lawmaker would also be and not be the lawmaker at the same time. This is absurd.
There exists a law without a lawmaker, therefore the major premise is false.

There is a moral law.
The burden of proof lies on the one who makes the claim that moral law exists. While people often behave in a like manner, not killing one another or stealing, this is not necessarily true for all humans. Some people DO kill and steal and feel no remorse. Morality is a trend in human behavior, however therh is insufficient proof to call it a law. The burden of proof lies with the one making the claim.

When someone steals from you and beats you up, if it is valid for them then don't complain.

The Creator wouldn't be Himself?

I'm not as sure about your first challenge, but your 2nd one is quite true. If there were a moral law, I'd imagine we could agree on it. Even the bible, supposedly a perfect, immutable book of god's word cannot lead to an agreement on morality, must be "reinterpreted" every so often to change to the culture's morality, and itself teaches many immoral things.

Why does the Bible need to be reinterpreted? It is as you say "immutable". The morality of God's word is agreed upon in those 66 books. I am glad you can't find anything as to your immoral claim.

Thus my wording "supposedly" immutable.

Thus why??