A note on barrel lining. The process is commonly done with .22's and low pressure calibers (e.g., .32-20) to give old rifles a new "lease on life". First the barrel is drilled out with a long drill that follows the old bore. Then the liner and bore are tinned (old way) or epoxied (new way) and the liner pressed in. The liner includes the chamber, but it may need finish reamed. The liner will probably need cut off or other finish work, like an extractor cut, done.
Now comes the problem. As long as the pressure is low, the liner itself is enough to stand up to the pressure. But the hole drilled or reamed in the barrel is not perfect, and there needs to be room for the solder or epoxy. If the pressure is too high, the liner will swell out into the irregular space in the original barrel and the result will be a swollen and bulged liner and an inaccurate barrel.
Another way is to bore or ream the original barrel to a thin shell and then insert a new barrel, thick enough to withstand high pressure by itself. That is feasible in some cases, but much depends on the original barrel profile. The process is sometimes called "sleeving" since the original barrel becomes a thin sleeve. Both systems will preserve original markings on collectible guns.
I may be wrong, but AFAIK, those C-96 pistols were worked over in one of two ways, neither of which involved lining. Either the barrels were reamed out to 9mm bore size (.346") and re-rifled, or the barrel was cut off ahead of the receiver part, the stub drilled out, and a new barrel inserted. Either was quite feasible; I doubt lining (as generally understood) would be.
Jim