My father often quoted "As idle as Litherum's dog".  Can you find out
where this quotation came from, who Litherum was and the significance
of his dog?

Dear researcher225,

Without much doubt, the saying your father often used was a curtate
corruption of an old English proverb: "Lazy as Ludlam's dog, which
leaned has head against the wall to bark."

This old saying related to Ludlam, the famous sorceress of Surrey, who
lived in a cave near Farnham, called "Ludlam's Cave." She kept a dog,
noted for its laziness, so that when the rustics came to consult the
witch, it would hardly condescend to give notice of their approach,
even with the ghost of a bark.

The notable corruption of "Ludlam" to "Litherum" indicates that your
father knew the proverb from oral tradition only. Such immense
shifting is typical for tradition by hearing.

Source:
Bootlegbooks: The Dictionary of Phrase and Fable
http://www.bootlegbooks.com/Reference/PhraseAndFable/data/735.html

I would like to point out that my Fellow Researcher, pinkfreud-ga, has
found this answer and generously allowed me to use it for this answer.

Best regards,
Scriptor

My question was answered quickly and clearly.  I was fascinated by the
story and the association my father had made, obviously through oral
tradition.  This answer was of great importance to me;  my father is
deceased and his children, my siblings, all use this saying.  Many
thanks indeed.