Frederick appears in the 1881 census, before he married Mary, living with his mother and siblings at Court 10 House 2, Birmingham, Warwickshire. His mother was a widow at that time.
Emma LAWLEY Head W Female 38 Worcester, England Charwoman
Frederick LAWLEY Son Male 14 Bham, Warwick, England Fancy Worker
Albert LAWLEY Son Male 12 Bham, Warwick, England Corkscrew Maker Half Time (Dom Imp)
Harriet LAWLEY Daur Female 10 Bham, Warwick, England Scholar
Emily LAWLEY Daur Female 6 Bham, Warwick, England Scholar
John R. KELLEY Lodger ((Boarder)) M Male 22 Wolverhampton, Stafford, England Laborer
Hannah KELLEY Lodger Wife M Female 21 Bham, Warwick, England Pen Maker
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Frederick and Mary appear in the 1901 census living living at 135 Barr St., Birmingham, Warwickshire. living with Mary's sister Sarah, and her husband Joseph Ashmead. There appears to be no children from the marriage.
Joseph Ashmead, 31, Cycle Polisher, Warwick Birmingham
Sarah Ashmead, 29, Grocer Shopkeeper, Warwick Birmingham
Rose Ashmead, 8, Warwick Birmingham
James Knibbs, 13, adopted son, Warwick Birmingham
Clara Knibbs, 24, boarder, cycle chain maker, Warwick Birmingham
Caroline Knibbs, 16, boarder, Metal Button Presser, Warwick Birmingham
Frederick Lawley 34 boarder, Cycle Fitter, Warwick Birmingham
Mary A Lawley 34 boarder, Cycle Lamp Presser, Warwick, Birmingham

James, Clara and Caroline are Mary's siblings.