Due to A) Queen Victoria having so many children and grandchildren as well as B) World War I, the 1917 Royal edict limited “royalness” to the children of the Monarch and the male-line grandchildren of a Monarch.
Of course the sitting King (or ruling Queen) can adjust that – prior to young Prince George’s birth in 2013, there hadn’t been a living Monarch who had a living Prince of Wales (Charles) who had a living heir apparent (William) who in turn also had an heir apparent (George) in a very long time, if ever.
Elizabeth did not amend the 1917 edict. She wrote out Letters Patent, specific grants of nobility (or in this case, royalty) to ensure George, and later Charlotte and Louis, were granted the styles of “Prince” or “Princess” and the right to be address as “His/Her Royal Highness”, since William was going to be the next Prince of Wales.
A good example of the status quo is HRH Prince Richard, the current Duke of Gloucester. His father was HRH Prince Henry, the 1st Duke of Gloucester, and his grandfather was HM King George V.
Prince Richard’s oldest son, though, is Lord Alexander Windsor. Once Prince Richard dies and passes the title, Alexander will become His Grace the (3rd) Duke of Gloucester. He’ll be a Duke, and that’s no small thing, but because his last royal ancestor was a great-grandparent, he won’t be a Royal Duke.
So to answer your question – assuming descent from younger siblings of a Monarch, no unexpected deaths/abdications, and no marriages to or inheritances from other royals or noble title-holders? Three generations to go from HRH to plain Lord/Lady, and a couple generations more to become a plain old Mister or Miss.
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