The trap monsters share a common trait: they look like something natural or wanted in the environment. Mimics shape-change to doors, chests, desks or anything else that would attract adventurers' attention. Piercers look like stalactites. Shriekers look like a larger fungus in an ecosystem where fungi is king. The Lurker Above looks like the ceiling in any underground room.
The Lurker Above predates modules, and even AD&D. Its first published appearance was in Strategic Review #3 (Autumn, 1975). Three other "trap monsters" made their appearance with the Lurker Above: Shambling Mound, Piercer and Shrieker. The other monsters included were: Yeti, Leprechaun, Ghost, Naga, and the Wind Walker (Expect a Monster Monday on this obscure thing!)
By this point, D&D was an underground sensation. And the clamor for more was readily apparent in the Strategic Review. Gygax was in full DM mode. He was scouring everywhere for more creatures (why else would the Leprechaun be statted?!) But, the trap monsters were a big hit. They make for interesting encounters.
D&D, in its earliest days, boiled down to characters versus environment. Monsters weren't antagonists, they were challenges. Lurkers Above and the other trap monsters cranked the environment's ruthlessness up. But, because each one is so specialized, it would be redundant to give you my typical "how I use this" section. Instead, I will leave you with a partial list of the trap monsters that show up in my campaign.
Living Statues (and golems)
I also use disease creatures (green slime, rot grubs, cerebral parasites and others.) But, that's a different topic.
When you get ready to use a trap creature, always make sure you are describing whatever they are mimicking several rooms before the party reaches the surprise. You hope their guard is down by the time they reach the room. And they don't get to complain about "no warning."