This shadow is alright, though I was more thinking of a shadow like the one you rendered. To do this one, we can use a perspective transform to be at the bottom of the icon. The pen is not in the same direction so it needs to be done separately.
By doing so, the shadow will definitely go outside of the image, so I moved the pencil a bit. Also I stretched a bit the sky-blue drop.
I rendered it in 512x512 pixels. I've put the files in lazpaint/icon folder.
Can you render it in 1024x1024 with your brand new blender?