I was interested in your question and I have done some digging around, but, like you, I have found nothing to explain why the medallion was struck on the centenary of the naval action. I looked at these two websites:
http://www.nmmprints.com/image.php?id=392598
This is the National Maritime Museum website, which shows your medallion, and offers for sale prints of it. Perhaps you might get some information from the museum. I noted the artist/maker is given as C & S Co., so I looked for that on Google, but found nothing. The other website is:
http://query.nytimes.com.
This shows the New York Times of June 2nd 1913, with a report of a service to commemorate the centenary of the death in the action of Capt. Lawrence of the Chesapeake. I did not read all the article, but in the piece that I did read, there was no mention of a medallion.
I'm sorry that I can't be of any help, and I suppose that you have already seen these two websites, but I shall keep looking. Best of luck.