The condition that Lady Margaret and her daughter Lucia are suffering from which is hereditary, causes them to have difficulty reading, muddle left with right and write letters and numbers the wrong way round, is never named; but it is almost certainly dyslexia, which produces all of these effects.
Most likely Lucia Galloway's dog, Mr. Gillespie is named after American jazz trumpeter John Birks "Dizzy" Gillespie, since Lucia was a fan of this musical style.