Very nice rifle, nice to see it made it back home. Just a couple of observations for you:
Looks like the nose cap has been cleared so not interfere with the muzzle. My guess is for target work(?)
The two pics below illustrate. The second pic is of a MKIII heavy barreled (H) target rifle, with the inside of the nosecap "opened" up. The first pic is of a standard LithgowMkIII*. I checked my other Mk III's, which include 1913, a 1919, and 1921 dated Lithgows. All the nose caps fit tight around the muzzle.
Perhaps in the past, your rifle had been a club target rifle. The barrel has been changed at some point in its life.
Either way, its a nice looking rifle. Congratulations!