move pasted shape so it is offset from original shape
fill pasted shape with pattern
adjust edges of pasted shape to align with original path.
You never need to create a diagonal line pattern in Illustrator. Simply create a vertical or horizontal line pattern, then apply it to a shape and use Object > Transform > Rotate. Untick the Transform Objects box (the Transform Patterns box will auto-tick) and enter the angle you want the lines. This is much easier than creating actual angled patterns. (Photoshop can't do this in case anyone is wondering).