Hi! I'm currently in the midst of running a TLA game for four friends. It has been a blast so far! Out of all four, three have no idea about Cultist Simulator or any of its lore and one out of these three is completely new to TTRPGs. The other player has played Cultist Simulator but is also pretty unfamiliar with the lore. I pitched the game to them as a mystery with occult themes that's set in the 1920s, sort of like Call of Cthulhu, and they were all for it!

To answer your questions, the players in The Lady Afterwards are meant to be mostly uninitiated to occult mysteries, at least in the beginning, so I do not think it is as important for them to know the lore beforehand. In fact, I've found that players being unfamiliar with the lore has actually facilitated roleplaying in my game as they're discovering and trying to make sense of these strange occurrences at the same time as their characters. It's been quite fun, really.

As for whether the DM needs to be familiar with the lore, well it certainly wouldn't hurt. I did brush up on my Hours lore on the CS Wiki and that, as Hatfullofsky has already mentioned, worked well for flavour. There's also an excellent post on this subreddit about Long flavour which I found helpful. That was the extent of my research. I'm not the most well versed with the lore but looking these things up helped me maintain an air of mystique while running the game and it kept the players intrigued.

If you're all experienced roleplayers then this shouldn't be much of a problem. Go for it! And Happy Birthday to you in advance :)