ya , as claven2 said, recess crown.
the flat bullet base suggestion is also worth a try as I know , many of these rifles like the flat base bullets.
This thread is of interest to me because a bit of a hobby of mine is finding lithgow sporters that have no restorable value as far as collectors go. Most are already shortened a bit or drilled and tapped for a scope like the weaverT0-1. I give them new purpose as hunting rifles after a make-over.
The lithgows can be very good rifles and are known to have thicker barrels and 5 groove bores which theoretically equates to better accuracy. This is the main reason I suggest having the crown looked at ,because I have been down this road many times with lithgow barrels.
The 2 groove barrels definately seem to perform better with the flat base bullets but with those 5 groove barrels, I have also had excellent results with spitzer boat tails. Worth trying though for sure.