The French LaBelle rifle was the first to use copper jacketed bullets, I believe around 1890. The copper isn't just to look good. At speeds of about 1100 fps and above, i.e. supersonic, lead fouling of rifling becomes very significant. Good modern 9mm and .40 handgun rounds are right around this point.

If you shoot hot loads or other guns with higher muzzle velocities and use only non-jacketed lead, it won't hurt your gun. But you will have to clean it more often and more thoroughly or it will affect accuracy.

BTW, the LaBelle was also the first rifle to use boattail bullets.