Q delivered his lecture on the life and poetry of Lord Byron at University College, Nottingham in 1918. He delivered his three lectures on Shelley in Cambridge University in the autumn of 1921. They were first published in 1922 in Studies in Literature: Second Series by Cambridge University Press.
At the time he delivered the Byron lecture, Q was very preoccupied with the end of the First World War, in which his son was fighting. He was also extremely concerned about the effect that the war was having on society in general. Profiteers and manufactures were benefiting from the conflict while the establishment was using the war to silence independent voices, like his own.
Q felt strongly about the current political situation but chose to express his views by making parallels with historical characters. Byron was still a controversial figure a hundred years after his death. Q saw him as a figure who had his faults but who suffered at the hands of conventional society. In Shelley, Q saw a genius who exposed the mediocrity of a materialistic society.
You can read a full study of the lectures here.
You can also read the lectures for yourself here.