To see if a coupon code has been used, log into the admin side of lmscheckout and go to Commerce>Coupons. You will see a list of all of your coupon code groups. Click on "view" for any one of them and the group will expand and show each of the codes in that group.
From there, next to each coupon code there will be an indication on whether the code been used or not. There is not currently a search function for coupon codes right now, so it is a manual process to see if they have been used. There is pagination in the group as well so it only shows 50 or so at a time.
One way to see find a specific code is to click ctrl/cmd F on your keyboard which opens up a page search function. Enter the code you are searching for there, and then page through the codes and your search box should let you know when the code shows up on the page. From there it is relatively easy to find.