Fentanyl's therapeutic index is NOT 270 except when used as an opioid supplement for surgical anesthesia cocktails, where the dosage is less a microgram per kilogram and it's balanced with several other drugs and opioid antagonists. The maximum recommended dose for fentanyl is 50 mcg/kg and that requires ventilation because it is well above the estimated LD50 of 30 mcg/kg. The recommended low dose for fentanyl on its own is 1 mcg/kg so at best we're talking about a therapeutic index of 30.
LSD's therapeutic index is unknown because its LD50 has never been established in humans or monkeys and you can't extrapolate from non-primate animals to humans (for example, rats can handle a dose of fentanyl that is a thousand times higher per kg than monkeys can, which is where many of our LD50 estimates come from).
Glad I could enlighten. The therapeutic index is a very subjective measurement that makes some drugs sound safer (or more dangerous) than they really are. Both the numerator and denominator in the ratio are very situation dependent. For example, trazadone is a hypnotic at doses in the tens of milligram but an anti-depressant at doses in the hundreds of milligrams so depending on what you're using it for, its therapeutic index could be different by up to 100x.
Likewise, in a clinical setting (i.e, with a trained anesthesiologist in fentanyl's case), the dose at which 50% of patients die from a given drug is usually much higher because trained professionals can quickly receive feedback by monitoring the patient's symptoms and apply drugs or medical devices to keep them alive well beyond what could kill someone on the street.
LSD's therapeutic index is unknown because its LD50 has never been established in humans or monkeys and you can't extrapolate from non-primate animals to humans (for example, rats can handle a dose of fentanyl that is a thousand times higher per kg than monkeys can, which is where many of our LD50 estimates come from).