The line is from the song 'Sunset Soon Forgotten' by Iron & Wine.
Do you think it originally comes from sentences like 'Let this sunset be soon forgotten' or 'May this sunset be soon forgotten' or does this sentence have the acient subjunctive structure like this?
Be this sunset soon forgotten
First, let's talk about other similar patterns for which the meaning is clear. A medieval Irish poem has a familiar English translation starting "Be thou my vision, O Lord of my heart." In this case, it's a simple imperative. "Be the thing that fills my sight." The pronoun "thou" (old familiar version of "you") is thrown in mainly to fill out the poetic metre.
A similar one is the Robert Frost usage in the linked question: "No bird is singing now, and if there is, / be it my loss." This is also a sort of an imperative, standing for "let it be my loss," which is itself a sort of roundabout future tense, "it will be my loss."
Another usage would be a conditional. In the tale of Jack and the Beanstalk, the giant uses rhyming verse to announce that he smells a human: "Be he alive or be he dead, I'll grind his bones to make my bread." Here, "be" is used archaically where we would just use "is," and there is a conditional using an implied "if": "If he be alive [or dead], I'll grind his bones." If this were the intent, then "Be this sunset soon forgotten" would be followed with some consequence. "If this sunset [were to] be soon forgotten... [then this would happen]."
But we don't find that. The song lyric is short enough to quote in full here:
Be this sunset soon forgotten
Your brothers left here shaved and crazy
We’ve learned to hide our bottles in the well
And what's worth keeping, sun still sinking[Refrain]
Down and down
Once again
Down and down
Gone again[Verse 2]
Be this sunset one for keeping
This June bug street sings low and lovely
Those Band-Aid children chased your dog away
She runs, returning, sun still sinking[Refrain repeats]
You ask about "this sentence," but many of these lines are not sentences; we have a collection of sentence fragments. As is often the case in poetry, we are left to guess at the missing fragments, or even without creating a meaning, we "harvest" emotions that are triggered by the connotations that the words and phrases raise for us.
Overall, the tone and theme of the poem seems to be nostalgia for childhood memories and concern over their fleeting nature. The speaker recalls details, some of which are aesthetically pleasing ("low and lovely,") and some of which might have been less pleasant at the time: hiding the evidence of underage drinking might be a fond memory or a problematic one, and "your brothers left here shaved and crazy" could be a complicated story that we're not told, or could perhaps suggest that they grew up and left town, perhaps enlisting in the military (where their heads are shaved), or simply as adults who have to shave. Regardless, some parts of these memories are "worth keeping," and like sunsets, they both subside ("sinking," "down and down,") and persistently return ("once again").
This context doesn't fit a reading of the first line as an imperative. I don't think the author wants these sunsets to be forgotten. Furthermore, the start of the second verse suggests the memories should be kept. If it is to be a conditional, the rest of it is missing and left to the hearer's imagination. But this doesn't fit well either, because the point seems to be that these sunsets can not be soon forgotten. At the most adventurous, I might read it as the same as "Be thou my vision": an imperative telling the listener to "be" the sunset, to embody the cycle of fading and returning, to inhabit the persistent memories. But this does nothing to remove the same problems the other readings have.
Ultimately, while we can define some common uses for this pattern, this poem doesn't fit any of them well, and while it evokes a certain mood, the line in question doesn't communicate a single clear meaning.
