Is lsd associated with depression?

Yes. One of the more serious consequences of using lsd is persisting delusions or hallucinations that destroy normal function. That itself leads to serious depression and even suicide. Additionally depression can directly come from the use of lsd. It seems to have the same pattern Cocaine has - within 24 to 48 hours after coming down from the high, severe suicidal depression and suicide can occur.
Very possible. Depression is associated with all forms of addictions.