There's nothing wrong with lead, it's the profile of the bullet that makes the LRN bullets a poor choice for self-defense.
You don't have to move up to the high-dollar SD rounds to make a huge improvement. You can stick with a lead projectile, just use something besides LRN. Flat nose, semi-wadcutter or wadcutter lead bullets are far better choices for self-defense than LRN. The old semi-wadcutter hollowpoint bullet was quite effective, and that bullet can still be found in a few loadings. I believe Winchester offers it in .38Spl +P.