All cars on the parking lot means, every single car. No car is being excluded in the previous example. Any car on the parking lot means, any specific car on the parking lot, but not every single one of them.

They define a different way of looking at a collection of things, ideas or objects.

Note that I say "Any car", as I am referring to a single car and not several or more.

Your specific question requires more of a context to answer properly. I cannot provide your answer right now, but I will explain any vs. all below as best I can.

"I want any of the food on the table", makes me picky.

"I want all of the food on the table", makes me greedy.

Use any for a specific instance of a group, any kid, any bus, any car, any word, any answer, and use all to mention every instance of a collection.

"All" means every one of the available choices. "Any" means some subset of the available choices. Depending on context, it may mean just one, or it could mean that more than one is allowed.

"I'll take all of the candy in that box." If there are 30 pieces of candy in the box, then I want 30 pieces.

"I'll take any of the candy in that box." If there are 30 pieces of candy in the box, then I don't care which you give me, you pick one.

As it stands, all is used for a declarative sentence like the one you posted:

There was something false in all this.

and Any is used to make an interrogative sentence about the same topic:

Was there something false in any of this?

It may vary depending on other examples.

The short answer is that "all" refers to the whole of something (if uncountable):

I've drunk all the water from this glass.

or the whole of a collection of things (if countable):

I know all the students in this class.

and "any" refers to some amount of something (if uncountable):

I've drunk some water from this glass.

or one or more things of a collection of things (if countable):

I know some students in this class.

I imagine the reason that makes the example:

There was something false in all this.

confusing is that "some" and "all" appear in the same sentence.

To dispel the confusion, one has to understand that "all this" and "something false" do not refer to the same thing.

Let's put the example into some context. Imagine, for instance, that I'm a mathematician that has written a proof for some impossible theorem. In this context, "all this" means "the proof", that is, the whole chain of reasonings that led me to the impossible theorem. "Something false" is the part of the proof, that is, the reasoning or reasonings in the proof that are wrong and that led me to a wrong conclusion.

One could also ask whether it's possible to use "any" in the example (since "something false" refers to some amount of a something).

The answer is yes, but bearing in mind that "some" is used in affirmative statements, and "any" is used in negative statements and questions. For example:

There wasn't anything false in all this.

Was there anything false in all this?

Sometimes, Any rather emphasizes there are no exceptions. For instance,

'It is important that Member States encourage any deck crew member who might need to navigate the craft to have training and certification regarding the operation of such radios.'

This phrase uses any to show that ALL the crew members, regardless of their qualities, shall have the training (as long as they might need to navigate the craft).

To that end, the answer by Mnescat claiming that 'any car in the lot means, any specific car on the parking lot, but not every single one of them ' is not quite comprehensive as any car in the lot might mean all the cars in the lot, regardless of their properties, that is, every single car in the lot. For example: any car in the lot is subject to parking fee (all the cars are subject to the fee, no exception applies)