Day 4 - Straight position lower back gap

During the Straight (Supine) position, should the gap between the lower back and the floor disappear if you have a good posture?
What I mean is.. should the lower back touch the floor without any effort after some time of practice?

If I understand your question correctly, no, it does take some effort to do this, but at first it can feel like it takes an enormous amount of effort.

The body will naturally want to have that lower back arch, it's normal and good to have, however for GST we learn to manipulate this 'natural' shape into the other shapes, which will always take some amount of effort to do.