I try to be careful when talking about "lining" the barrel of a high power rifle. When the term "liner" or "lining" is used, most people think of the thin liners sold by Brownells and others for use with .22 or low pressure center fire cartridges like .32-20.
But the liner itself must be thick enough to contain the pressure involved so when you talk about lining the barrel of a rifle in the higher pressure ranges, you can't use one of those liners. The liner for a high pressure rifle is essentially a light weight barrel inserted into a thin shell which is the old barrel drilled and reamed out. Of course, the composite barrel will not (cannot) be as strong as a replacement barrel would be, though it has to be at least adequate for the maximum working pressure of the cartridge.
If you try to use a thin liner for a cartridge in the 35-60K psi range, at best the liner will bulge into any and all gaps between it and the original barrel, resulting in poor accuracy. At worst, the liner will not be strong enough and will burst, which will probably burst the shell of the original barrel also. I can't recommend trying to line the barrel of high power rifles. If they are collectors' items, they should not be fired anyway and should be left alone; if they have no collector interest, they should be rebarrelled.
Jim