"I just let mine eyes with your eyes meet" means "I just let my eyes meet your eyes." That makes sense to me.
"I just let
my eyes with your eyes meet" means "I just let my eyes meet your eyes." That makes sense to me.
That's what the last line means. I can summarize the last two verses in a few lines.
1- When I want to say "I love you".
In verse number 1, I am talking about my feeling, which is beyond a shadow of a doubt is "love, how I express it.
2- I let mine with yours meet,
Since the poetry starts or vitally focuses on eyes, it is needless to say/write your eyes or my eyes according to their placements in the 2nd vers. For instance: I let my eyes meet your eyes. That sounds right but distastes rhythm, alliteration at the end of each verse and the flow of poetry. As this poetry has a few more verses, which I still haven't dropped here, talks about eyes it was/is needless or redundant to lengthen the 4th verse by saying "my eyes meet your eyes".
I hope it's all clear, now.
I am not a great poet but have a bit of knowledge about poetry. I like being guided whenever I make mistakes in English, here. I wish to be guided more.