Well, I think perhaps you'd need to go through some tutorials to get a grip on the basics.
That said, there are many methods you can use to do this. For organic shapes, you can use t-splines in Fusion 360, and combine those with objects created from sketches, but you can (as you mentioned) also use lofts to make organic/flowing shapes.
A dome can be created by sketching a half circle and then revolving it, but to mate that to a rectangular shape like your bottom case, you'd need some transition. You can also create a rounded shape by lofting just a few sketch curves.
The very simplest method to create a dome-like lid for a box is to loft a surface to a point, and then thicken that and combine cut with the bottom half. I've attached a very simple example, it's just a handful of operations on the timeline. The resulting shape has creased edges from the corners of the bottom half, but you could of course loft with rails and more sketches to avoid that. As I said, this is just a very basic example.