While at Jesus College, Cambridge, Montgomery was a member of the Footlights, its amateur theatrical club. Subsequently, she studied at the Central School of Speech and Drama. Montgomery built her career as one third of Comedy Theatre Company Population 3, along with James Bachman and Barunka O'Shaughnessy, and she appeared as a roving reporter for the comic television programme The Friday Night Project. Other television work has included Bo' Selecta!, The Mighty Boosh, and The IT Crowd.

Montgomery has been heard in several Radio 4 programmes, including the radio phone-in spoof Down the Line, Robin and Wendy's Wet Weekends, The Way We Live Right Now, The Museum of Everything, The Department, Another Case of Milton Jones, The Party Line, Harry Hill's Ghost of a Christmas Present, The Pits, the Torchwood story "Lost Souls" and Lucy Montgomery's Variety Pack. She produced a pilot for her own sketch show pilot for the BBC called The Full Montgomery which went on to run on Radio 4 for two series.