Wordy, but fun to write.
From context, "smoking-room stories" means something like off-color stories, dirty stories, steamy stories. One dictionary entry for the adjectival form of "smoking-room" glosses it as "Marked by indecency; obscene: smoking-room humor."
If you google "smoking-room humor" you will get many relevant hits, of varying degrees of sordidness. (All subsequent examples were found this way.)
At one extreme, an odd 1899 novel My smoking room companions by William King, apparently devoid of sordidness but full of piffle. Only slightly more relevant but more fun to read is Mark Twain's 1898 Following the equator, where in chapter 1 he describes the captain of an ocean liner:
Our young captain was a very handsome man, tall and perfectly formed, the very figure to show up a smart uniform’s finest effects. ... He avoided the smoking room. He had no vices. He did not smoke or chew tobacco or take snuff; he did not swear, or use slang or rude, or coarse, or indelicate language, or make puns, or tell anecdotes, or laugh intemperately, or raise his voice above the moderate pitch enjoined by the canons of good form. When he gave an order, his manner modified it into a request. After dinner he and his officers joined the ladies and gentlemen in the ladies’ saloon, and shared in the singing and piano playing, and helped turn the music. ... The electric lights burned there as late as the ladies and their friends might desire; but they were not allowed to burn in the smoking-room after eleven.
Here there is no statement of anything improper in the smoking room, but the fact that the captain preferred the gentilities of the ladies' saloon to the smoking room does allow us to surmise that tobacco, slang, puns and anecdotes, etc. might be found there. (Chapter 2 also has a smoking room episode.)
Other hits are more to the point. Jean Harrell's 1995 Caravagio and his two cardinals has this zinger:
Perhaps the most generic token of how group nudity evokes boasting is the phrase "locker room humor," which seems to survive, while the synonym "smoking room humor" has faded as women took to smoking.
This usage is found in a 1990 report of a 1943 law case against Esquire magazine:
Postal authorities called only nine witnesses, drawn largely from Washington society, to prove its claim that Esquire's smoking-room humor overstepped the bounds of mailability. Clergy played an important role. Among the many clippings in the case file is one that shows the Methodist resident bishop of Washington, Edwin Hughes, eyeing the Varga girl for April 1943. The bishop is quoted as saying "I wouldn't care to exhibit this in my Sunday School class."
From all of this I would conclude that Harrell's description is close to what Lewis had in mind.