The only difference I can see anyone agreeing on is that “lots of” is more informal. In theory, “lots of” is more than “a lot of,” as there are multiple theoretic “lots.” In practice, though, they are interchangeable. Except I think “lots” often carries a bit more emphasis on the large number.
At least, that’s the feel I get in your example. I can’t even read it without putting a slight bit of emphasis on “lots of” that I don’t put on “lot of.” (Technically, I say “lotta” and “lotsa.”)
A ‘lot’ is a collection of things. For example, one might go to an auction and buy one lot of knick-knacks. Or they may buy two lots or three lots or whatever.
So when I hear ‘a lot’, I think of ‘much’ or ‘many’ of the thing being mentioned. When I hear ‘lots’, I think of many lots of many things. i.e., One lot vs. multiple lots.
Rather then quote the entire post, I’ll summarize: there are times when “lots” refers to frequency while “a lot” refers to quantity. The example is “I’ve eaten lots today” vs “I’ve eaten a lot today.” The first is only frequency, while the second can also refer to quantity.
The same post also indicates that there is a construction “That’s a lot of” that cannot be substituted with “That’s lots of.” The example given is “that’s a lot of water,” compared to “that’s lots of water,” which I agree sounds completely unnatural, and would only work in contrived situations.
And, yes, I’m aware my “summary” is longer than the post in question. Consider it an explanation instead, as I think I explained it better.