When Davos Seaworth sees the axe, he thinks to himself that Lady Lu is the biggest axe he has ever seen, with the sharpest edge Davos has ever seen. The other keepers at the Wolf's Den claim that Garth spends his days honing the axe.
A Dance with Dragons
While in captivity, Davos Seaworth is shown Lady Lu by Garth, one of the keepers of the Wolf's Den. Garth tells Davos that when Davos's hands and head will be cut off, it will be done using Lady Lu.