The answer is simpler than you think: soap is uncountable.
In English, soap is conceptually a mass, a lump of homogenous material, which is typically not a countable noun.
However, many mass nouns, if not all, can be made count by
treating the plural as units of the thing (bars of soap). For example, if you "drink three beers", that means three bottles / cans of beer.
treating the plural as "types" of the thing (brands of soap). For example, if you "use three soaps", that suggests three different types of soap, not three bars of soap.
So you might have encountered plural "soaps" somewhere, but it would be one of the above cases.
As Michael notes in a comment, you could also read it as an ellipsis for "that brand of soap" or "that kind of soap". I'm inclined to think he's right (otherwise "that soap" suggests some predefined quantity somewhere). But note that the resulting phrase "a lot of that brand of soap" is logically a metathesis of "a lot of soap of that brand", which brings us back to the uncountability of soap.