It depends on what the existing bore diameter is and what you want to use in the liner. Let's look at an example.
Say you have a 6 pounder (bore diameter 3 5/8" more or less), a 3/8" liner would take you to 2 7/8" bore. Assuming a chamber pressure of 10,000 psi, the hoop stress in the liner would be 43900 psi which is approaching the nominal tensile strength of mild steel. The stress value is directly related to chamber pressure so if that is 25% higher, the stress is 25% higher.
If we reduce the liner bore diameter to the forum recommendation of 1/3 of the overall diameter, that would give us a bore of 1.2" and a corresponding hoop stress value of 12,500 psi, which would easily be contained by the liner alone.
Now if you had to have a 3" bore, you could have the 1.2" chamber and still be OK.