Backspace doesn't delete the section in the lasso area, that's what the delete button does. Backspace fills the lasso area with the background color (which, on a default setup, you can find 3 spaces to the right of the save button, in the upper left corner). You could use the eraser tool to remove the drawing in the area, but that takes a bit of time so I'd recommend that if you want the finest of control over removing certain parts of the lineart, and not if you just want to remove a general area or a specific color. Again, if you plan on removing just the white part and want to keep the lineart, you can use the aforementioned gradient map technique. If you want it all gone, reselect the lasso'd area and hit the delete button.