A tale of two freemasons - The King's speech

One of the plot summaries of the story as stated on IMDB

In the mid 1930s, King George V is concerned about the immediate future of the British monarchy. His eldest son David, first in line for the throne, is in a relationship with American divorcée Wallis Simpson. Marriage to a divorcée and being King of England (and thus head of the Church of England) are incompatible. King George V's second son, Albert (or Bertie as he is called by family), second in line for the throne, speaks with a stammer, something he's had since he was a child. Although a bright and temperamental man, Bertie, because of his stammer, does not capture the confidence of the public, which is paramount if Britain does enter into war against Hitler's regime. As King George V observes about living in a communications age, a king can no longer get by in life solely by looking good in a regal uniform and knowing how to battle riding a horse. Elizabeth, Bertie's loving wife, wants to help her husband gain confidence solely in his increasing need to speak at public functions, regardless if he becomes king or not. She finds an unconventional Australian-raised speech therapist named Lionel Logue to help assist in curing Bertie's stammer, with no one, even Lionel's family, knowing he has this job with the royal highness. Lionel and Bertie's relationship is often an antagonistic one as Lionel feels the need for the two to be equals during their sessions - with Lionel even calling him "Bertie" instead of "Your Royal Highness" in their sessions, which doesn't sit well with Albert, not used to such familiarity with a commoner. Lionel does in time become Bertie's confidante and friend, especially from Lionel's side as he tries to determine the psychological issues behind the speech impediment. An issue with Lionel (which he does not hide but also does not fully disclose) may threaten their relationship altogether, which may be especially problematic as a still stammering Bertie ultimately becomes King George VI and Britain enters into war with Germany.

- Written by Huggo / edited by statmanjeff

The film's storyline was during the 1930's and took certain liberties with its historical accuracy and that is probably why the Freemasonic connection between the two main characters was left out. 

Bro. Logue was installed master of St George's Lodge (now JD Stevenson/St George's Lodge) in Australia during the year 1919. 
(Freemasons: Tales From the Craft by Steven L. Harrison)

Bro. King George V had been Initiated into Freemasonry an English Lodge but later became Grand Master Mason of the Grand Lodge of Scotland. He rarely had any difficulty while performing masonic ritual.The extent of Freemasonry's influence can be seen in this quote:

After the Second World War, King George wrote that ‘Freemasonry has been one of the strongest influences on my life’ and in collaboration with engraver Reynolds Stone helped create a postage stamp, part of the ‘1946 Victory Issue,’ which is filled with masonic symbolism.

1947 Victory Stamp

Even before they met for the first time they had something in common - Freemasonry.So it was not just a therapist treating a patient who was also the King. It was also a brother helping a brother improve himself.