How to make soft shadows and lift them up?

How can I achieve such shadows in ThreeJS?
I only got shadows like in the second image.

try following contact shadows example.

I think contact shadows is what he already achieved. (the second image).

Perhaps add a directional light or spot light that casts shadows?

it’s not clear to me what you mean by “lift them up” … if you want regular shadows you need a light that casts them from whichever direction.