Does anyone know how law schools treat American citizen's with an LLB from the UK? Is one considered a domestic applicant by virtue of citizenship alone, or is it based on if you attended a domestic law program in the US only?

I guess they will treat you as "an applicant who hold a law degree from a country outside United States".

That is correct. However, because you are a citizen, assuming your foreign law degree meets the legal education requirement, you will be eligible to take the bar in states that require US citizenship or permanent residency status.

Hi!
I have a friend in the exact same position. I think she was treated as foreign degree holder. So yes, it matters where ur llb is from and not so much ur citizenship.
Since there are few American citizens with a foreign law degree applying for an LLM, I'd say youre chances are pretty good!