He attended Holmlea Primary School in Cathcart (now closed) before being evacuated to Troon in 1939 at the start of the World War II. In 1942 he returned to Glasgow to join Weir Pumps Ltd in Cathcart, Glasgow (then called G. and J. Weir Ltd) as an Apprentice Marine Engineer. While an apprentice he also studied for the Higher National Certificate exams at Langside College in Mount Florida and, following this, left Weirs to study full-time at the Royal Technical College, Glasgow (now the University of Strathclyde). He graduated with a BSc in Mechanical Engineering in 1950, and was winner of the Montgomerie Neilson Gold Medal and Prize (awarded to the first ranked graduating student in Mechanical Engineering).
He rejoined Weir Pumps and in 1954 he became Head of Steam Turbine and Gearing Design, in 1962 was made Chief Designer and in 1966 Director and General Manager of the Pump and Turbine Division (later renamed the Energy Division). In 1980 he became Director, Contracts Division at Weir Pumps before moving in 1988 to take up the Managing Director role at Weir Westgarth Ltd until his retirement in 1991. He was Chairman of Clairmont Plc from 1992-1994.
He was a Fellow of the Royal Academy of Engineering, President of the Institution of Engineers and Shipbuilders in Scotland from 1987–89, Fellow of the Institution of Mechanical Engineers and Fellow of the Institution of Marine Engineers. He was conferred Honorary Fellowship of the Institution of Engineers and Shipbuilders in Scotland in 2004.
Thomas Leith was active in the local community. He was Chairman of the Community Council in Newton Mearns and, following a move to Strathaven in Lanarkshire on his retirement in 1991, was actively involved in the Avondale Civic Society of which he was Chairman from 1998-2004. A plaque near Strathaven Castle was raised by Avondale Civic Society to commemorate his contribution.
- T.O. Leith; H.E.C. Clapham; J.R. McColl (September 1969). "Glandless Pump–Motor Units for Feed Heating Plant in Central Power Stations". Proceedings of the Institution of Mechanical Engineers, Conference Proceedings. 184: 19–29. doi:10.1243/PIME_CONF_1969_184_345_02.
- T.O. Leith; J.R. McColl; M.L. Ryall (September 1969). "Advanced-Class Boiler Feed Pumps for 660-Mw Generators". Proceedings of the Institution of Mechanical Engineers, Conference Proceedings. 184: 36–47. doi:10.1243/PIME_CONF_1969_184_422_02.
- A. Linstrum; P.G. Nicoll; G.C. Mulholland; T.O. Leith (November 1995). "Large Seawater Reverse Osmosis Installations in Gulf Waters and a Process Comparison with Multi Stage Flash Distillation". Proceedings of the IDA World Congress on Desalination & Water Sciences. V: 27–41.
- Former Holmlea Primary site, Evening News, 4/12/2009
- Transactions of the Institution of Engineers and Shipbuilders in Scotland, page 366, Vol 46, 1903
- US patent 3128714, George Frederick Arkless & Thomas Orr Leith, "Centrifugal pumps", published 1964-04-14
- GB patent 77501, George Frederick Arkless & Thomas Orr Leith, "Improvements in or relating to centrifugal pumps", published 1964-12-09
- GB patent 836146, Thomas McAlpine & Thomas Orr Leith, "Improvements in or relating to boiler feed pump installations", published 1960-06-01
- GB patent 891161, Thomas McAlpine & Thomas Orr Leith, "Improvements in or relating to the control of feed water pumps", published 1962-03-14
- GB patent 801618, Thomas Orr Leith, "Improvements in or relating to apparatus for indicating and/or controlling the level of liquid in a container", published 1958-09-17
- "No. 51171". The London Gazette (Supplement). 31 December 2007. p. 10.