FindMyPast doesn't have war diaries. The only records they have for GGrandad are a link to the medal card at the National Archives and to his Commonwealth War Graves entry (both already quoted) and a reference to the publication "Soldiers Died in the Great War".
The war diary can be downloaded from the National Archives for £3.50 (already quoted) but is on Ancestry at
http://www.rootschat.com/links/01orl/For completeness Ancestry has:
His medal card
His medal roll entries (one for the 1914/1915 Star, the other for the British War and Victory medals)
His entry in the Effects Register and the Soldiers Died entry.
A pension record card (for his wife) is on Ancestry but in the Fold3 area which requires an extra subscription
These are all listed here:
http://www.rootschat.com/links/01orm/His battalion was part of 46 (North Midland) Division. Google will find you a number of histories of the division which would put the Lincolns war in context. Check the dates covered given that GGrandad was with them in France from October 1915 to April 1916.
His service record itself has not survived (60% or so were lost to bombing in WW2). From his number though we can say he joined up, as a volunteer, in March/April of 1915.
MaxD