i think you can:

• Convert line vertices to points(line_points).
• make voronoi polygons using the points(line_points).
• dissolve the resulted polygons using either an id attribute which has been saved from line layer  , or by a spatial join with line layer.

i wish i have really understood your question  , if not you can you provide a drawing, to explain more your needs.

I think you can:

• Convert line vertices to points(line_points).
• Make voronoi polygons using the points(line_points).
• Dissolve the resulted polygons using either an id attribute which has been saved from line layer, or by a spatial join with line layer.

I hope I have really understood your question, if not can you provide a drawing to explain your needs more.