There's a story unravelling in the poem. I understood someone likes melancholy rather than uplifting stories. I am not quiet sure. But I like the images of the silver hair and the lavender eyes.

Dashiel, I love how all your poems hold a mysterious tone to them. I always wonder if you are writing about a girl or it is someone you always dream of meeting. I loved this poem though overall. It's great imagery kept me wanting to read more. I loved how you used the sky and all the imagery to be your muse in this as well. I agree with Lucero there does seem to be a story enfolding here and it holds beauty. Well done

There is much behind the poem which only the writer knows. I can see a graying old woman with beautiful eyes soaked in sadness when there is so much beauty to be seen and felt around her.

A moving write where the writer's voice is heard by the reader..well penned.

**I just want to warn you that this comment is going to be full of (hopefully) constructive criticism. I'm sorry if I come off as harsh.**
It definitely seems like this poem has a lot more meaning for you than what we readers can get out of it. That is definitely a stylistic choice that you can make, but can I say that in this case I wish you would give us more insight?
From multiple read-throughs I think this poem is about wanting to write a poem for someone else, someone you care for very much, but who tends to be a bit sardonic (morbid laughter, yes?) and maybe a bit of a melancholic daydreamer, but you don't think you can write anything good enough to please them. Instead you decide to write about them. Is that right? I like the thought, and like other commenters have said, the description of lavender eyes is striking.
What I think you should do with this poem is to go back and reassess the structure. First of all, I think that by having the line breaks be so choppy you're doing a disservice to your imagery. Instead of focusing on the phrase that you've written, the reader focuses on individual words, and the meaning is lost. I had to take out the line breaks to read it properly. Line breaks can really be an excellent device in a poem, but if you're going to use them, my personal preference is to use them strategically: to highlight the phrases you want to stand out, and to encourage the reader to breathe with your poem.
For example, in the second stanza, the structure makes the poem read: "what does (pause) it take (pause) for my story (pause) to rhyme (pause) with time (pause) when in (pause) every beating (pause)..." etc, you get the point, I think? Reading it makes me feel a little woozy, like I can't breathe properly. Instead you could try phrasing it as "What does it take for my story to rhyme with time (pause) when is every beating of my heart, (pause) your lavender eyes seem to rust (pause)..." etc. To me, the words become more lyrical and the images are more engaging. I think the meaning would become more clear and the poem would become more accessible, as well.
My other suggestion would be to go over each sentence carefully. I like the descriptions you're creating (ex: "you only want a dream that is silvering the melancholic sky" ... that is a beautiful line). However, you've crossed some metaphors to the point where I'm not entirely sure what you're trying to say. For instance, I really don't understand the first stanza.
"To capture a moment designed with your pleasing smile and morbid laughter, I get a paper that lost its metaphorical meaning when the last autumn dream falls."
The issue is part grammatical, but I also think you've used too many words to describe what you want. "To capture a moment designed with your pleasing smile and morbid laughter" is already too complicated to be readily understood. I like the idea of designing a moment so that someone will smile for you, but I think that "pleasing" weakens the image of what the smile is to you, and I think that the structure of the sentence could use reworking.
I think a good exercise with this poem would be to look at each sentence. Ask yourself, what are you trying to say, specifically, and see if you can put that thought into words in a sentence that doesn't use any large words. Next, try to integrate the two. Does the line in your poem accurately match what you intended? Do all of the metaphors and descriptions you've used service that description, or do they confuse or detract from it? Those are the sort of questions that will help this piece.
I do think you have some really powerful lines in this piece and the overall thought is a sweet one, but I think you should work on it some more to improve on it. Hopefully nothing I've said has offended you. Genuinely just trying to offer constructive criticism. :)