Insert the lining into the shell, right sides together. You should see the seam allowances on the outside and on the inside of the bag. Pin all around the edges, but leave a gap about 4 or 5 inches wide at the bottom of the diagonal (see pictures). This is the opening through which you will turn the bag right-side out.
Stitch where pinned, with 1/2" seam allowance. Clip the curves.
Reach into the gap and turn the bag right-side out.
Fold the raw edges of the gap inward and pin to match the rest of the edge. Topstitch close to the edge.