No, this is not a question about how to make Quaternion.Lerp work. I did figure out the how part. I also figured out why it seemed to not to work. However, once I figured the problem, it seemed clear to me that this may not be what I wanted. Allow me to explain. During my studies, it became clear that Quaternion.Lerp was creating a deformation on my object. My solid is a parallelepiped. It is longer than it is wide. In spite of the fact that I was rotating my solid 90º to the side, the start object and the end object are exactly the same, hence why I thought no rotation was happening, at all. I ran it slowly using the Lerp third argument as a public variable so I could control it on the Inspector and it became obviously clear that a deformation of the object is happening. Nowhere when people talk about this, they seem to mention that it happens. So, how to make it not happen, please.
I imagine Quaternion.Lerp is used to interpolate between a start and an end rotations. An alternative to this would be using Transform.LookAt method onto an invisible game object that would then follow whatever you want to rotate onto. That following mechanism would then be one more aspect to it: moving radially (which would mimic the Quaternion.Lerp); smoothly following with inertia; etc.
Solved the problem. It seems that the issue was with the fact that it had a parent, and followed its dimensions instead of its own. You must unchild it for it to work correctly.