The Behavior

When you enter y=40, time begins ticking.
You will begin to hear cave sounds, and eventually, it will spawn.
(The Lurker replaces nearby common mobs like zombies, so if the area is mob-proof, it's lurker-proof.)

The Cave Lurker behaves erratically, it may attempt to sneak up on you, running away when spotted, or just chase you relentlessly until it decides to leave.

While chasing you, if you can get it down to half health, it'll run away, unless you have been scaring it off too often, in which case it will instead be stunned for some time, creating an opportunity for escape. Just try not to do it too much, the Lurker might not like that.

This isn't just a fast guy kill you, it comes with drops.
Using these drops, you can craft two powerful items, and a block to ward off any further attacks by the Cave Lurker.

The Drops

When stunned or killed, it will drop teeth, which can be used as an alternative to bones.

When killed, it may drop an eye, which can be eaten, although it will give you momentary blindness, and it's not very filling, either.

Tooth Necklace

The Tooth Necklace is worn on the head, and while it provides no armor value, it will give you haste while standing on natural stones! (Stone, Granite, Diorite, Andesite, Tuff, Calcite, Deepslate and the ores.)

Deep Stew

Deep Stew is a powerful food item, having high food and saturation values.
It also gives you haste II, night vision, strength I, speed I, and health boost II for almost five minutes.

Lurker Repellent

Lurker Repellent will prevent lurkers from spawning in a 160 block radius from where it is placed.