Your curves are broken up into segments and Loft wants to use whole curves. There is a command called "Merge" that is not in the UI, but it did not fully work here when I tried it. If you use the Join command once you selected all the edge curves on the shape, you'll get one closed curve that Loft likes.
Play around with Loft's settings to figure out what kind of point matching works best. When I tried with Profiles: set to "Auto" the loft result had a funky shape to it.. "Exact" worked better.

Two other methods include grabbing all of the edge curves and Joining them as single rings in their respective objects;

1) You can then perform a Loft on each ring. Make sure to use the "Exact" setting on the "Profiles:" list. So that the shapes use the existing curve points. (middle)

2) You can also place a curve at any point to bridge the two shape rings. Then perform a Sweep, selecting the two rings when asked at first. (top)
I made the bridge curve (which is really called a "Profile") with a FreeForm curve. The ends have to snap to somewhere on the rings of your shapes and should be adjusted to be more tangent or flat with their respective edges. The Sweep takes the shape of the curve and swings it around the "Rails" or the edges of your shapes.
Then you can go back using the History state of the Sweep to tweak the bulge as you can see below:

Network is a very good choice.

Note: Blend can be done, but is tricky. Could be done piece by piece if the two sets of edges have curves that start and end in the same relative places.