I walk and walk, arriving at a lakeside ¶
A gentle breeze blowing to the lake, rippling my mood ¶
Glimmering sunshine, makeing my inner world warm ¶
White gulls glide through, herons swimming and hunting ¶
Love this sereneity, far from citie'sy noise ¶
Look far on the other side of the lake ¶
Layers and layers of blue peaks're lik are showing up in hazy wearther ¶
Behind tall reeds, transparent water lap quitetly at the shore ¶
At this moment, I wonder if I'm with you, the one I miss at night ¶
That would be howmake me glad even though ¶
I knew you were not with me from the outset

Verbs should generally be consistent in similar phrases/lines. For example: "glimmering" would match in form with "making", whereas "glide" matches with "swim and hunt."

"Serene" is an adjective that has to be talking about a noun. "Serenity" is the noun form. In the sentence "Love this _______," the blank space needs a noun or noun phrase. Another way would be to say, for example, "Love this serene environment."

You could say "cities´ noise," but "city noise" means "noise from the city or cities."

You could say "layer after layer of blue peaks shows up" or "layers and layers show up" or "layers and layers are showing up"

"transparent water" is a singular noun, so it should be followed by "laps" instead of "lap"

"that would be how glad" is unusual phrasing. Maybe the way I corrected it is close to your intention.

I walk and walk, arriving at a lakeside ¶
A gentle breeze blowing toacross the lake, rippling my mood ¶
Glimmering sunshine, make my inner world warm ¶
White gulls glide throughoverhead, herons swimming and hunting ¶
Love this sereneity, far from the citiey's noise ¶
Look far on the other side of the lake ¶
Layers and layers of blue peaks're like showing up in appear through the hazy weather (or "are seen through the hazy wearther ")¶
Behind tall reeds, transparent water laps quitetly at the shore ¶
At¶
In this moment, I wonder if I'm with you, the one I miss at night ¶
That would be how glad even though ¶
I knew you were not with me from the outset (-> I'm not quite sure what you mean in this sentence)¶
I knew you were not with me from the very beginning ("outset" doesn't feel very poetic, so I changed it to "very beginning")