If you select just the edges that you want to connect, turn them in to a group, then draw an edge(or an arc/curve) on each end to bridge to gap to create 'closed geometry', you could then use Soap Skin & Bubble and get a mesh created.

You could also use Curviloft: Select just the edges that you want to connect, turn them in to a group, run 'BZ Polyline Segmentor' to create equal segments on both edges, then run Curviloft to bridge the gap.