Lenzie is a small affluent town by the Edinburgh and Glasgow Railway in the East Dunbartonshire council area and the historic county of Dunb…Lenzie is a small affluent town by the Edinburgh and Glasgow Railway in the East Dunbartonshire council area and the historic county of Dunbartonshire in Scotland. It is about 6 miles north-east of Glasgow city centre and 1 mile south of Kirkintilloch. At the 2011 census, it had a population of 8,873. The ancient barony of Lenzie was held by William de Comyn, Baron of Lenzie and Lord of Cumbernauld in the 12th century.