In 1975, Lowry was appointed by Merlyn Rees to chair the Northern Ireland Constitutional Convention, an unsuccessful attempt to replace the collapsed Sunningdale Agreement.
In 1977, John Hume challenged a regulation under the 1922 Civil Authorities (Special Powers) Act (Northern Ireland), which allowed any soldier to disperse an assembly of three or more people.
[2] In 1980, Lowry partly excused the actions of two members of the Royal Ulster Constabulary (RUC) convicted of murder and bombing by stating they acted under the "powerful motive... that more than ordinary police work was justified to rid the land of the pestilence which had been in existence".
[6] This was criticised by the Historical Enquiries Team of the Police Service of Northern Ireland as "difficult to conceive of a statement more fundamentally flawed or calculated to destroy the confidence of a large section of the community in the court's independence and probity".
He also presided over the supergrass trial in 1983 where Kevin McGrady, a former IRA member, gave evidence which led to the conviction of seven out of ten defendants.