That's a lot of ___ vs. those are a lot of ___

We can consider "a lot of cars" as a plurality of cars, and use those.

We can consider "a lot of cars" as a singular "lot", and use that.

Synesis or notional agreement is where we use a grammatical number not of what is plainly stated (the plurality of cars) but of what is implied (the single "lot"). The fact that "a lot" contains a singular article (a) adds to this implication.

A significant thing here is that we are focusing upon the concept of lot as important in itself. Because this is what we are remarking upon, we're more inclined to consider a lot than cars when matching the number.

Conversely:

A lot of cars have cruise-control.

*A lot of cars has cruise-control.

Here we're focusing more upon something to do with the cars themselves. For this reason the plural form sounds clearly correct, while the singular sounds wrong.

A lot of sweets is an okay present if you can't think of anything else.

*A lot of sweets are an okay present if you can't think of anything else.

*A lot of sweets are okay presents if you can't think of anything else.

Here we're focused again upon the singular "lot" of sweets, and further making of it a single present, and singular agreement works while plural does not.

That is singular and those is its plural counterpart. While it is more natural to say that's, it is incorrect. This is a common grammatical mistake regularly made by almost everyone. This error has become so common that it just sounds/feels weird to say "those are a lot of people" instead of the more common "that's a lot of people." Part of the reason this may feel so awkward is because we tend to be lazy speakers and we like to use contractions as often as possible. We don't have a contraction for those are, these are, there are, so instead we have become conditioned to (incorrectly) say that's and there's, even when the subject is countable and plural.