Il était là toujours means nothing. You need to switch là and toujours : the second sentence is the correct one and the only one you would say.

Il était toujours là can be translated as he was still there with the first explanation you provide, but forget the first sentence we don’t say that in any way, that’s not grammatically correct, even with a comma after là

Là and toujours are both adverbs. In what you want to express là modifies the verb être and toujours the adverb là.

Theoretically adverbs can be placed before or after the verb. It’s most usual to have the adverb after the verb but it can depend on the length or meaning of the adverb.

It’s correct to say :

J’étais là.
J’ai été là.

An adverb that modifies another adverb is always placed before the adverb it modifies. Therefore toujours when modifying là will always be placed before là. You can consider that “toujours là” is a sort of idiomatic phrase.

Je suis toujours là.
J’ai toujours été là.
J’ai été toujours là.

Are all correct.

Note that when in a compound tense toujours can be placed before or after the past participle but will always stay before là even if separated from it by the past participle.

Il était là toujours
is not only ungrammatical but not even a mistake a French native would make.

If you come across toujours after là it will be in a context where toujours does not modify là and the punctuation will be different from the one in your sentence.

Il était là, toujours prêt à aider.

In this last sentence toujours is placed before the sentence it modifies, i.e. “prêt à aider“; “toujours prêt à aider” is apposed to “Il était toujours là” and separated from it by a comma.

An example with encore:

Il était encore là.
Il était là, encore à se plaindre.

First off: the first one is grammatically incorrect, and thus doesn’t mean anything.

On the other hand, the second one is interesting. In French, “still” and “always” can both be translated to “toujours”.

You could have:

Deux heures plus tard, il était toujours là-bas.
(Two hours later, he was still there.)

But also:

Il était toujours là pour moi.
(He was always there for me.)

And only the context will help you know which one is being used !