The lines method + loft that Stefan shows may be the easiest...

You wont' be able to use the "Closed" option in Loft because that tries to make a regular closed surface and in this case you want opposite corners of the surface to be touching instead.

So leave a small gap in the surface, and then fill in the gap with a second step - one convenient way to fill in the gap is the Blend command - hide the line cross-sections that were used to make the Loft surface and then you can select the ending edges of the loft and run Construct > Blend to build a smooth surface between them filling it in.

- Michael