So I've recently learned about absolute phrase and wondering if we can use it with adjective like:
Lanterns hang from the branches, the night sky visible through the spaces between the leaves.
Is that correct?
Lanterns hang from the branches, [the night sky visible through the spaces between the leaves].
Preliminary point: absolutes are not modifiers but supplements, loosely attached expressions presenting supplementary non-integrated content.
They consist of non-finite clauses that contain a subject and have no syntactic link to the main clause.
Your example has no verb, and thus it's a verbless clause, though I would still call it an absolute construction; more specifically it's the verbless analogue of:
Lanterns hang from the branches, [the night sky being visible through the spaces between the leaves].
Incidentally, the verb in the absolute clause can also be a past participle, as in
That done, [she walked off without saying another word.]
This will be a long answer, but I hope that it will also be useful for others who have similar questions.
A nominative absolute (that is the term that I prefer, although there are certainly others) has the following characteristics:
You asked about whether the adjectival phrase could be headed by an adjective, and the answer is yes. In fact, most kinds of phrases that function adjectivally can be used. Let's consider several kinds of heads.
Our car broken, we had to cancel the rest of the trip.
The car running smoothly once more, we resumed our trip.
Its gas tank empty, the car finally came to a stop.
Its radiator on the fritz, we abandoned the car.
Our destination yet to be seen, we despaired of ever arriving.
The following are rare and perhaps questionable grammatically, although I know of no rule prohibiting them.
Possessive case noun:
The car John's, I had no right to question what he wanted to do with it.
Possessive case pronoun:
The car his, John had every right to decide what he wanted to do with it.
The only such kind of phrase (i.e., one that can function adjectivally) that can not normally be used as the second element in a nominative absolute phrase, as far I'm aware, is an attributive nominal. (Attributive nominals typically precede their referents.) You might construct something like this, although I probably wouldn't consider it grammatical:
?The car's weight 1000 pounds, we didn't want to push it to our destination.