That's a nice Derr rifle you have there! And actually, in pretty nice original condition!
I know some say to leave it as is, while others think replace the missing parts and make it look a bit better, more complete. Generally speaking, for working guns like this one, a complete rifle is valued more than an incomplete one as this is. Unless there is some compelling or historically known reason to keep it as is, ( say Jessie James held the owner up, and stole the inlays out of the rifle
replacing the missing parts would add to the collectability and overall look, and value of the rifle.
To that end, the missing inlays are easy, though time consuming, to replace. They are either silver or German silver, so the correct metal need be used. The missing patchbox door and side plates are relatively straight forward to replace, though again, time consuming to replace. Judging from the remaining part, there was just minimal engraving around the edge. As for the lock, the rifle has most likely always been a percussion rifle, and never a flintlock.
By the time D. Derr made this rifle percussion was all the rage, and this lock shows none of the hints that it was ever a flintlock. Some of those hints are a single lock bolt construction, engraving on the forward end of the lock plate where the flint pan, frizzen and frizzen spring would have been, and no filled in screw holes for those parts.
All in all, you have a nice rifle!
John