It’s my understanding that alcohol and all the drugs like LSD and cannabis were banned under the League of Nations Opium Act, why weren’t cigarettes included?
It's a good question, but I'm not sure there's a clear answer for it. I'm not sure which act you're talking about in the question (Hague Treaty or Geneva?) A lot of substances were on the chopping block between 1875-1940, but as a general rule a lot of them were racially targeted, too. They had a colonialist logic for prohibiting alcohol, opium, hash, and cocaine, but tobacco was too central to Euro-American culture (which, if we are talking about the League of Nations, that's who is calling the shots). Some people were gunning for caffeine (including the guy who founded the FDA), but there wasn't enough of a moral panic over it to convince people to abandon and ban tea, coffee, etc. The number one thing that alcohol, hash, opium, and cocaine all had in common though was that people were convinced that they drove people insane and led to rape, disease, crime, inefficient labor, slavery, and medical immorality (in the sense that immorality was treated as a medical symptom). But neither tobacco nor caffeine carried the same stigma. Tobacco also has a significant commercial presence in that era, so my guess is they couldn't get a ban to fly for that reason. I've found plenty of sources that wanted to ban tobacco too, but they couldn't make it stick. That's my best guess for this anyway and I've gone through the relevant collections at the National Archives, if someone has a more concrete answer I would be delighted to know the source.
Also the League of Nations regulations were too early to consider LSD. The LON was gone before LSD was really a thing.