If these are the correct parents, here is Lily in the 1901 census:
21 Kincardine Street, St Peter, Dundee
282/1 ED 22 Household No. 44
James Tarbet, 47, jute mill mechanic, b. Forfarshire
Ann, 42, mechanic's wife, b. Perthshire
Maggie(?), 18, jute weaver, b. Dundee
Lily, 11, scholar, b. Dundee
Gadget