Summoning Engine/Mad

If the Enigma is the true, original form of The Other, as some have theorized, this would mean that Lucrezia herself at one point became posessed by the Other. Since we see Lucrezia attempting to become good at one point, and this is apparently sincere, because she only drugs Klaus' drink, and spirits him to parts unknown (presumed to be Skifander for a number of reasons), rather than killing him with a lethal poison, her posession by the Other would have had to have taken place after that point.

In that case, the Other in posession of Lucrezia has full access to Lucrezia's prior memories.

But the Lucrezia personality posessing Agatha cannot remember things known only to Agatha, nor can Agatha remember things known only to Lucrezia.

The fact that the Summoning Engine was imperfectly constructed at the time Agatha had the Lucrezia personality applied to her could be an explanation of this.