As mentioned, you did not actually almost die at all. A number of trips I've taken had me thinking or feeling like I was going to die, sometimes I even believed it. But psychedelics have profound effects on perception and thoughts. Believing you're dying is not equal to actually almost dying.
Some psychedelics can in fact kill you, some at outrageously high doses and some (like the NBOMEs) can at reasonable dosages, so with some it's possible to be actually close to death... but LSD has one of the highest safety profiles of of any drug, psychedelic or otherwise. The only recorded death from LSD was when a guy intravenously injected 300mg (3,000 times a standard dose), thinking it was speed. The method of death was due to vasoconstriction, not being unable to breathe.