It is owned and operated by the Town Hall.
So far, since the town has no mayor, it has no name. However, the RL oldest pub in Lancaster, which has been there since the 1400s, is known in 2009 as the Three Mariners, and used to be known as the Carpenter's Arms. I'm basing the rest of the description on the assumption that this is the same place. http://www.threemariners.co.uk/index.php?Homepage
Just north of the Castle, on Bridge Lane (the corner of China Street & St George's Quay). It's on the same rock as the Castle, and uses water from there to ccol the cellar (which is upstairs: beer here is gravity-fed).
We have discovered that it has a dart-board - though beware of playing if Eve23 is present, as she tends to throw her sword instead of the darts.