From what I know of LSD (not having tried it) most of the bad effects are due to impure product, substituted product (i.e. it wasn't LSD) or wildly improper dosage.
Unsurprisingly, this is what happens when ANYthing is illegal and therefore all usage is uncontrolled. Look at alcohol during prohibition. It was frequently tainted with methanol, ethelyne glycol and god knows what else. Many people went crazy, committed horrible, violent, harmful acts or died suddenly because they drank tainted product. The major harm from illegal drugs stems from the very fact that they are illegal.
If drug purity and content were controlled and dosage information were freely available, the reduction in harm from these drugs would drop significantly. People who are going to do drugs are going to do them if they are legal or illegal. But if they were legal and controlled, people would know what they were getting, they would know how much they could do and they would be more likely to seek help if they had problems without fear of jail time. And far fewer people would commit crimes to get their next fix.
Yes, there would still be abusers and harm done, just like we still have chronic alcoholics, but the harm to the general public would be much less.
So no matter what your grandma said about LSD abusers there are far more reasons to legalize and have some control over drugs than to leave them in the murky shadows of the underworld.