What do the directions say about finishing the edges of the apron? Are they supposed to be hemmed? Is the 'lining fabric' just a solid piece or does it have the outline of the apron on it too? Is the 'lining fabric' plain or does it have a similar print on it? Is it possible the 'lining fabric' is for co-ordinating place mats?
If the 'lining fabric' is plain, considering the curves on the sides of the apron, I would make the ties and attach, then cut the lining to match the apron, with right sides together, sew all the way around leaving a small opening--probably on one side--turn right side out, press, and perhaps do a decorative stitch all the way along the edge.