LSD, like certain other hallucinogens, is a serotonin analogue, and its immediate effect comes about through binding to serotonin receptors, in particular one called the 5-HTP2A receptor. Since any meaningful discussion of this requires a certain degree of background knowledge:
> "In terms of visual perception, the 5-HT2A receptor has been found to play a role in modulating the processing of visual information. Specifically, activation of this receptor has been shown to enhance certain aspects of visual perception, such as the perception of brightness, contrast, and spatial frequency. This effect is thought to be mediated in part by the 5-HT2A receptor's ability to increase the activity of neurons in the visual cortex, which is the part of the brain that processes visual information."
> "Interestingly, the 5-HT2A receptor has also been implicated in altered states of consciousness, such as those induced by psychedelics like LSD and psilocybin. These substances are known to activate the 5-HT2A receptor, which is thought to underlie their profound effects on perception, thought, and emotion. However, the precise mechanisms by which 5-HT2A receptor activation leads to these effects are still not fully understood and are an active area of research in the field of neuropsychopharmacology."
So, let's consider the question raised in this post, which is: "how a could a temporary substrate-receptor interaction result in a long-term effect that persists well past the biochemical elimination of the drug from the user's system?"
I don't think this is uniquely applicable to LSD vs. any other drug, by the way. Some people might try an opiate-class drug once and develop an immediate craving for that experience. However, this really cannot be attributable to the basic drug-receptor binding - so it's probably something to do with neuronal rewiring of some sort. If neurons respond to the immediate drug experience by forming new neuronal connections to other cells, then this could explain how a long-term effect (visual snow, opiate craving, etc.) could be created by neurons seeking new connections in response to the short-term effect of one-time drug use.
Profoundly, it seems our brains are always rewiring themselves in relation to various stimuli and experiences, but LSD and similar drugs are affecting this process at fairly low levels in the neuronal hierarchy.
Note that this is precisely why many people have said that the psychedelic drug cohort, under controlled conditions, has unique potentials for curing various mental illeness-related conditions. The use of the potent hallucinogen ibogaine to effect long-term cures for opiate addiction is one such case:
https://pubmed.ncbi.nlm.nih.gov/28402682/
> "Conclusion: A single ibogaine treatment reduced opioid withdrawal symptoms and achieved opioid cessation or sustained reduced use in dependent individuals as measured over 12 months."