I would agree that it is a leap which is why I don’t see how you can get from 3 to 4, with 4 being God. It seems to hinge on the English words “law” and “lawgiver”, as if having the same three letters in each word means that they must be connected. It smells of conflation and equivocation.
If the “Lawgiver” were something as simple as logic and reason, that would be one thing. At least in my view, any being with the ability to feel empathy towards others and the ability to use reason and logic would arrive at a moral code all on their own. The way in which we judge morals is based on empathy and reason which gives rise to ideas of justice and fairness.
If we do follow the Moral Argument, you would also have to ask where the Lawgiver got those laws. It would seem that the Lawgiver would have to use something outside of itself to determine if the laws are good. If the Lawgiver simply chose morals at random with no source to guide them and programmed us to follow these arbitrary rules, does that sound like “goodness”? It seems that this would replace morality with obedience. It would also require an external set of standards outside of the Lawgiver to determine if his character was good.
I also don’t want to discount CS Lewis’ work sense he did make important and sincere contributions. Morality is a tough subject to dig into, and it has been a hotly debated topic since humans were able to debate.