What if LSD was so popular in our culture, that it would be used in a way similar to SOMA in Huxley's Brave New World? How would be shaped our civilisation?
Not likely, for several reasons. First being, each psychedelic produces a different experience. It's extremely unlikely for only LSD to be legal, so you'd have choices between mushrooms (quite a few sorts of mushrooms at that), mescaline, DMT, and anything you can think of. People are going to prefer different trips, basically.
Second, I doubt LSD could ever be so culturally important, because you have to devote significant amount of time to your trip. It's not something like alcohol or marijuana that is easier to incorporate into your daily life. For that reason, I think you'd instead have a society where most people have tried LSD out of curiosity, but the majority of people do not use it daily. Instead, only some groups of people (perhaps musicians or other "creative types") or subcultures would ever use it with any sort of regularity.
Lacking discipline, maybe yes, but creativity (how one would now gauge it?) might very well be higher. LSD radically changes thought patterns (both experienced but the changes can be seen using scans of the brain) and has been a key to at least some technological jumps. The research of Francis Crick is perhaps the most well known.Ewen Cameron would have to not be discredited. A mental restart. Our civilization would lack credativty and disipline