Born in Rockall, Dumfrieshire, Elizabeth was the eldest of 11 daughters of Margaret Dalzell, and Sir Robert Grierson, 5th baronet of Lag and Rockhall. She married Dr James Crichton, a physician, in 1810, after which Friars' Carse, Dumfriesshire, became her home. Widowed and childless in 1823, she became an outstanding benefactor to psychiatry as co-founder of Crichton Royal Hospital, Dumfries, and remained closely involved with its work.

Her main interest was in aiding people of her own class in reduced circumstances. She was described by her godson as 'a prim little lady... of a somewhat sombre manner... but genial and kindly withal, highly intelligent and well-informed'.

Since 1999, Crichton campus has housed satellite colleges of Paisley and Glasgow Universities on the former hospital site.