How Do I Remove Any Lines Without Any Thickness

I used the shape builder tool to knock off lines I didn't want. However, when I use the live paint bucket tool to fill in color, those invisible lines that were taken off interfere with the live paint tool, so this picture happens when it's not supposed to. I've tried using live paint tool selection, but that doesn't work for gradients because it fills in each surface with a gradient instead of having a single gradient throughout the selected space, Please Help!
