It could be "a lock of hair." "Lock" has many meanings. The commonest is a machine, operated by a key, that holds a door closed. But it can also mean "a curl of hair." And it can also mean part of a gun. And it can also mean the place in a canal where a boat is raised or lowered to a different level. "Twirling" a lock of hair would be twisting and untwisting it, wrapping it around your finger, and so forth. Alexandra, in your picture, it looks as if you might be twirling a lock of your own hair!

I have NEVER heard that phrase before. Was it in a sentence like 'he twirled the lock in his hands?' What was the context?

It means : unlock a lock by turning the lock around with a key