4 Military District (4MD) – South Australia and Broken Hill, Torrowangee, and Silverton in New South Wales.
Fairly rare survivor like I have said is the survival rate of the early rifles is directly related to how WWI was fought and their rate of attrition was a rifles life span was measured in mere weeks if not days whilst Lithgow had only really been producing the MKIII for 3 scant years starting production in 1912.
To be honest if you have taken the bedding away what other mods have they done to it I'd give it a good clean and drink of RLO/Mineral Turps put it all back together and see how it runs before you get tinkering, my friend uses a 1915 Lithgow and cleans up allot of shoots.
It can be seen on the bottom wood where the bedding compound was used it looks/appears like they relieved the very front near the front sight (Lighter shade) and opened up the channel where the muzzle would sit.
Would be interesting to know if they have done this as the front area is pretty important with regards to the bedding there there is supposed to be an element of up lift, I am sure the persons who know these rifles inside out will assist you in this matter.
Besides the modern projectiles have a whole different trajectory so the sight settings you'll have to figure out with range time just do the usual checks with the bedding & draws but if you replace the missing parts take the time to research the info on this site there is plenty here.
Have fun, I used my 1916 Lithgow MkIII 5 MD for shoots but decided that it should be a safe queen as the others in the nest are allot younger so they can do the range time like I said the early Lithgows whilst not abundant are a good catch.