Early Life
Lincolnshire Pedigrees1 describes her as daughter of Sir
Roger Kelke of Kelke in Yorkshire.
The
Visitation of Lincoln2 (acr 72) has a Kelke tree but doesn't include Alice - my theory is she is daughter of
Roger Kelke and
Ellen Inglebert, and that her aunt Isabel married her father-in-law William (his second wife perhaps, as his first wife was apparently the daughter of John Grovall of Harpswell).
Others have also had some trouble establishing exactly who Alice's father was: see
here. The author of this thread suggests that Alice's father Roger was actually the great-grandfather of the Roger I describe above, and who is shown in the
Visitation to have married ___ Leyburne, daughter of Sir Henry Leyburne. A lot of confusion arises from the mention in the
Visitation pedigree of the Isabel Kelke who married William Tirwhitt and whether this Isabel is the same person as Alice, or not.
Footnotes
[1] Lincolnshire Pedigrees, Rev. Canon AR Maddison, Volume 3, Harleian Society (1904); Tyrwhit of Kettleby, p1018
[2] Visitation of the County of Lincoln in 1562-4, ed. Walter C Metcalfe, London (1881); Kelke, p72