Wait, a burger in Kittery, Maine for National Lobster Day?. National Lobster Day is today, September 25th, and this burger is the most unique way to celebrate. When you think National Lobster Day, you probably think of a big ol' pot of steaming lobsters. But have you ever had a lobster cake on a hamburger? Of course, you haven't because Harbor Burger Shack in Kittery, Maine had to invent it!