Lace is the traditional AND modern material so definitely a gift with lace in it, or with a lace them, is right on target.
Great ideas for lace would be clothing, accessories like scarves, or a floral arrangement with Queen Anne's lace. Filigree lace jewelry would be a perfect match for the 13th anniversary!
Lingerie can be a really fun and spicy gift for your wife, but do keep in mind that some women have mixed feelings about lingerie. Many love it, and some are ambivalent. A few might even dislike it. It would be impossible for us to tell you which category your wife fits into so our advice is, if you are unsure, play it safe and get lingerie as the second gift rather than a primary gift. If she loves it and wears it often, then you will know for the future!
For the couple, gifts might be decorative tablecloths, curtains, or other lacey home decor.
For jewelry, either go with a lace design in any material or choose a piece with the alternate 13th anniversary modern materials of citrine, moonstone, or hawk's eye. Another option is blue lace agate or crazy lace agate which aren't traditional to the 13th anniversary but are certainly on theme with the lace name. Ultimately it's up to you and what piece you think your wife will most enjoy wearing!
For gifts to give your husband, skip the lace. But you probably already figured that one out! :-) Move right on over to the alternate material textiles and get him a top or other fabric gift with the logo of his favorite sports team, a funny t-shirt, or other clothing.
Fur is another alternate modern material, but please, only choose faux fur! Don't support what is quite often an unregulated, illegal poaching industry in foreign countries. Please only buy products that celebrate the beauty of Earth's creatures...alive!