I have fired the Navy Arms .32 Long Rimfire cartridges in S&W No. 1 1/2 and No. 2 revolvers with no apparent damage or harm. I wouldn't fire a ton of them, but if the gun is in good shape, I don't think a few would hurt.
BTW, the old guns shoot pretty well, though the sights are very hard to use.
-------
As to relining, it just means drilling out the old barrel to a given diameter and inserting a liner (a thinner inner barrel) that has the rifling cut into it. After the liner is installed, it is chambered. Done well, the liner is almost invisible and can renew a worn out barrel. For several reasons, conventional lining will work only with low pressure cartridges like those being discussed here.
Liners can be obtained for .22, .25-20, .32-20, .38-40, and .44-40, and maybe others, but those are the ones Brownell's has.
Jim