Keep in mind, the original barrel can actually be little more than a decorative sleeve if your liner is large enough. There are limits of course.

Remember the thickness dimensions of the liner and the drilled out old barrel are accumulative. The liner will be made of modern steel inside the old steel original. The combination will most likely will be stronger than the original

How thin the walls of the old barrel should be in drilling out the old bore for the liner should be determined by your gunsmith and how he drills out the old barrel. The walls can be quiet thin.

I have a barrel I am going to send off to John Taylor for lining. The liner is .630 in diameter, the muzzle of the barrel to be lined is .710. That will leave a wall thickness of .040, not a problem.

It isn't infinite however and you and you should discuss it with your gunsmith first.