Since a line created with the Line tool can only have one line segment (unless you mean you grouped it with other such lines), I don't know what kind of shape you'd mean.
Attach a screen capture of what you're talking about, as well as your InDesign version and operating system.
Your black figure is made from 12 straight lines, right?
You can select any two of them, than Object>Path>Join (or use Pathfinder palette for it).
Select resulting shape + another line next to it, again Join.
Repeat this till all your lines will be joined to single figure. Now you can fill it.
Btw, the better way to draw this would be to start with regular rectangle, and reshape it adding anchor points.
the Line tool only creates simple lines. A line with 2 anchor points always only has a stroke but not a (visible) fill color.
What do you need? You need a real shape. Please use the Pen tool and create your shape again. (The other but much more difficult way: merge your lines at every corner and change all several line into a closed shape)