If you are predisposed to schizophrenia, LSD may trigger your break. Then again, a stressful life event may have done it anyway, so it's not like it caused the condition.
Some issues may get better(depression?), some may get worse(anxiety?). We really don't have enough data to make recommendations on who should or should not do psychedelics. My personal experience was that I had a significant worsening of symptoms for several years(panic attacks, anxiety, bipolar swings). If I could rewind time and never do psychedelics, I would avoid them. However, now that I've done them more and have experience with how they affect me, I'm looking forward to doing them again when I'm retired and have time to recover.