The only information I have found about the 15th Battalion, Lincolnshire Regiment is a list of 3 names in the CWGC records.
RENTON, Alexander. Private, 39987. 15th Battalion, Lincolnshire Regiment, Transferred to :- Private, 30940, 52nd Company, Labour corps. Locre Hospice Cemetery, West Flanders, Belgium. Friday 19-10-1917. Age 32. Son of William & Helen Renton of Duddo Farm, Norham-on-Tweed. Husband of Mary Elizabeth Renton of New Harperidge, x Cornhill-on-Tweed, UK