Lung problems are not a side effect of LSD usage. The page you linked mentions "lungs" in an unattributed throwaway with the word "may", but I found absolutely no evidence of this in actual scientific literature.

Humans have an immense amount of experience with LSD and we know that in humans it has a very low toxicity.

Don't get me wrong - LSD is a strong drug with profound effects, and negative psychological effects are possible, but physically, there's no record of it causing toxicity, except that there appears to be a small but significant connection to mitral valve malformations in long-term use.

Of course, dolphins have a very different body chemistry, so we can't be sure, but dolphins in captivity often don't live very long, LSD or not, so a likely rational explanation is that we humans killed this intelligent animal by keeping it in captivity and giving it nothing to live for. But being poisoned in an experiment is certainly quite possible.