His research focuses on matrix analysis and related fields, motivated by problems from vibration theory, numerical analysis, systems theory, and signal processing.
[2] Lancaster thereupon worked as an aerodynamicist with the English Electric Company until 1957, completing a Master's degree at the same time under the supervision of Louis Rosenhead.
[4] Lancaster served as Department Chairman from 1973 to 1977, and President of the Canadian Mathematical Society from 1979 to 1981.
He was elected a Fellow of the Royal Society of Canada in 1984, and was the recipient of the Jeffery–Williams Prize in 1991.
[5] In 2018 the Canadian Mathematical Society listed him in their inaugural class of fellows.