We just got back from the DLH, and I was told they don't have refillable mugs. There isn't a 24 hour counter service restaurant like you find at the resorts of WDW. There's a coffee shop that sells muffins, bagels, etc. and a fast-food place (Crocs and Bites) near the pool. There's also another place called the Captain's Galley, but I was told they're only open in the summer, so I have no idea what you could find in there.