The artist was born into a wealthy family in St Andrews, Fife, Scotland.  Much against parental wishes she decided to study art. From 1932-37 she attended the Edinburgh College of Art, establishing her own studio there until taking up an Andrew Grant Travelling Fellowship, first arriving in St Ives on 10th March 1940. From that time until her death, her working year was divided between times in St Andrews and St Ives, maintaining home and studio in each place, and travels abroad on painting trips with companions.

Her close circle of artist friends locally included Margaret MELLIS (of Edinburgh originally), Borlase SMART, Barbara HEPWORTH, Ben NICHOLSON, Bryan WYNTER, Guido MORRIS and Naum GABO amongst others in the modernist camp. Willie was a member of the CRYPT GROUP who exhibited work not found acceptable to the more traditional members of the St Ives Society of Artists, and therefore they could only obtain the crypt of the Society's Gallery, situated in a former church.

In 1949 she married the writer David Lewis (dissolved 1963), who later determined to train as an architect at Leeds School of Architecture. For one year (1956-7) Willie took up a teaching post at Leeds School of Art, at the end of which contract she returned to St Ives, living separately from Lewis from that time.  Her work grew in abstraction the longer she lived, and her artist statement from her biography defines that stand: 'Abstraction is a refinement and greater discipline to the idea: truth to the medium perfects the idea.' 

Willie held strong opinions about the difficulties of women artists 'in a man's world' and frequently complained of being overlooked and crowded-out by male artists with large egos (and often, in her words, of lesser talent).  In later life, she relied heavily on her companion and friend, Rowan James, as driver, cook, and framer of her work, as these were everyday nuisances which she had never learned (nor wanted) to do.

Though ultimately her achievements in draftsmanship, colour and form were increasingly recognised, and with this progress her forthright confidence grew, it seemed often to be never enough to satisfy Willie's need for recognition. Both the award of the CBE for her services to art, and her four Honorary doctorates late in life, at St Andrews, Falmouth College of Art, Plymouth University, and Herriot Watt, Edinburgh, gave her great pleasure; Dr Willie was an active and generous patron and member of the Hypatia Trust (1996-2004). In her will she framed the plans for the Barns Graham Memorial Trust, which operates from her former home at Balmungo, St Andrews, Scotland.  It is set up to preserve her work, but also to provide working studio space and financial aid for young artists. The Trust can be contacted at: www.barns-grahamtrust.org.uk .