I think it's time to rethink "lots". If lots of people are using "lot's" as a plural of "lot", then why shouldn't that be valid? Language, after all, is not static and if enough people use a new word or a new construction, the language changes.
You could say that the current rule is already inconsistent and confusing, but imagine for a moment that an apostrophe could be used to construct an acceptable plural form and think about this example: "The lot's dimensions are..." Now, "lot's" is both plural and possessive. Is that one lot or multiple lots with the same dimensions? The current rule may not be perfect, but it is clearly less ambiguous than the alternative.
I disagree with you because in this case, it's a matter of semantic structuring. The language should be free to change, but only when it doesn't conflict with how the language functions. In this case, "lot's" would kill how parts of the language is interpreted, and changing it would offer no clear structuring for the two various "lots" usages.
There are some exceptions - I, for instance, don't mind people who use abbreviations like "u" since they make sense contextually, and while something like "lol" is overused I think you could make an argument saying "lol" has become a usable verb or even a noun in the English language ("lolled" is also very fun to say out loud).
In your case, however, I've got to disagree, though I don't know why people saw fit to downvote you that hard. Perhaps it's because you opened with a definitive-sounding statement before raising arguments in support, though that seems a bit kneejerk.
About the semantic structuring: Valid point, but people (who are ultimately responsible for language change) tend to ignore such things.