CHTULHU ON THE TABLE
Lovecraft's works have quite a big representation when it comes to tabletop games both simple and those more complicated, there is also a tabletop roleplaying game directly based on his creations. When it comes to board games titles that you have to check out are: Mountains of Madness, Lovecraft Letter, Mansions of Madness and Cthulhu Wars.
BOARD GAMES
Most of the games of this type sadly have quite extensive list of rules and require a bit of time and knowledge to get into, but if you are after that step there is plenty of fun to be had. When it comes to me ones that brought the most of joy were Mansions of Madness 2nd Edition and Chtulhu wars.
TABLETOP RPG
It would be almost impossible to not create an Roleplaying game based on Lovecraftian Horrors, an tabletop version was created by Chaosium Publishing by the name of Call of Cthulhu. In the game itself players take action as a group of ordinary people drawn into the world of mysteries and unknown, the more players discover the less their characters are sane.
SIMPLE AND FUN
Luckily some of the creators of the games thought about people who don't really have that much time to get into board games as well, which is why Lovecraft Letter or Unspeakable Words are perfect choices. Lovecraft Letter is a social deduction game, since rounds in this one take just couple of minutes you will quickly pick it up. The other game - Unspeakable Words are even simpler - it's scrabble with some additional rules, each of the players draws 7 cards and takes turns trying to make words with them.