Yes, there really was a smoking room on the Hindenburg… even though the zeppelin was inflated with 7 million cubic feet of highly flammable hydrogen gas.
The smoking room was kept at a higher pressure than the rest of the ship so that no leaking hydrogen could enter the room, and the smoking room was separated from the rest of the passenger section by a double-door airlock.
The smoking room was closely monitored at all times by a member of the zeppelin’s staff, and only one electric lighter was provided; no matches, lighters, or other open flames were allowed anywhere on the airship.
In reality, the pressurization of the smoking room may have been as much for public relations as for safety. The smoking room was located on B Deck, at the bottom of the ship, and since hydrogen is lighter than air any leaking gas would have escaped upward. (It would have been very unlikely that free hydrogen could have settled downward to the level of the smoking room, and only a leak at the very bottom of the cell adjoining the smoking room in Bay 12 would have posed any significant risk.)
The real danger of allowing smoking on a hydrogen airship — and the reason it was strictly confined to the closely monitored smoking room — was the risk of a fire; had even the smallest fire started in the passenger section, it could easily have spread to the gas cells above, destroying the ship.
The smoking room was perhaps the most popular room on the ship, which is not surprising at a time when so many people smoked, but its popularity was no doubt enhanced because it was also the location of the Hindenburg’s bar.