I am trying to fill the white space in my art work using live paint. I select all of the art work and click in the space I want it to fill but it seems to only give me the option of filling the little black lines (see images below) instead of the white space around it I want to fill.
I guess the white area is empty and you want to create a shape which fills it. Your black frame around the white area has a gap or some part of it is not selected. The problem can be seen in the bottom. It looks like a black line is out of the selection.
If there was a piece which is not a path you would get a warning dialog.
I have wrestled with the same problem like an idiot when I forgot I had locked some parts. Check the Layers panel is there locked objects.
BTW. Live paint can accept also gaps. See Live Paint Gap options.