A major problem with a small lathe is drilling the bore of a cannon or howitzer (OK for mortars.) You are essentially limited to barrels half as long as the length of the lathe as the drill takes up its own length before the bore is started. Same problem if you bore the bore instead of drill it. Also the small lathe may not be able to hold the drill or have the power to drill a large hole.
If you are serious about getting a lathe to make your own barrels, look around for a Logan or South Bend of 36" length. They don't grow on trees but they are out there if you look hard enough. While they usually need 220V 3 phase, that is relatively easy to provide. You need that much size to be able to make a half scale mountain howitzer, which for me is about as small as I want to go, at least in a serious gun.