Roll-top desks were a popular piece of office furniture in the 19th century. Their allure to owners was their ability to temporarily file large amounts of paper and to secure working hard-copies by simply shuttering and locking a rolling door. Most of these desks included one set of matching keys. One key was to be kept on the owner's person, the other to be placed in a secure location. If you have a locked roll-top desk and no key, you can still open it.
Take two paper clips and straighten them completely. Bend one at a 90-degree angle, at a distance one-quarter or one-third from the end of the wire. Bend the extreme tip of the other paper clip at a 90-degree angle with needle-nose pliers. One paper clip should resemble an "L" shape, the other should look like a dentist's tool.
Slide the "dentist's tool" paper clip into the lock with the "tooth" portion turned upward to the back of the keyhole. Insert the "L" tool with the long side pointed to the floor under the other paper clip.
Push upward on the "dentist's tool" paper clip to test the deepest pin on the upper side of the lock. You should hear it move or click up and down as you apply and release pressure. Press up on the pin and set the "L" paper clip snugly below the other paper clip to catch the pin before it falls from its up or open position.
Repeat Step 3 until all four or five pins are prevented from falling from their up or open position. This will require a great deal of trial-and-error as well as patience. Once all pins are free, the roll-top desk should open.