His maternal grandfather was William Kirby Sullivan, and his paternal great uncle was John Blake Dillon.

Having initially undertaken the mandatory preliminary course in arts, Dillon decided to study chemistry and physics, receiving his BA in 1904.

[1] Dillon was appointed assistant to professor of chemistry, Hugh Ryan, at the Catholic University school of medicine on a salary of £6 a month.

During the 1913 Lockout, he was the honorary secretary of the Industrial Peace Committee, and was the chemical adviser to the Irish Volunteers in their manufacture of bombs and hand grenades.

He helped his father-in-law, George Noble Plunkett, convene a meeting of nationalist delegates from across Ireland in Dublin.

At the Sinn Féin convention in October 1917 he refused the position of secretary, and instead agreed to sit on the executive council.

After his release, he was appointed to the position in March 1919, after considerable opposition due to his IRB and Sinn Féin activities.

Dillon was often evading the authorities, so rarely stayed at home, and his wife was imprisoned for a time in Galway Jail.

[1] After the Irish Civil War, Dillon was able to focus on his academic career, and became an internationally respected expert in the structures of carbohydrates, specifically those in seaweeds.