Lunatic Cultist won’t spawn

I assume you mean the cultists that appear on the entrance to the dungeon aren't spawning. The Lunatic Cultist is the boss that spawns when you kill them.

First things first: The Lunatic Cultist is only available on the PC, Xbox one and Playstation 4. If you're not on one of these platforms, then you simply can't fight the boss. Sorry.

Assuming you're on one of these platforms, there are some things you can try:

• Try beating the Golem again. Who knows, maybe a bug caused it to not register properly (something like this once happened to me, when the Dryad wouldn't spawn after beating the Eye of Cthulhu. Beating it again solved the problem)
• The cultists won't spawn if you placed walls in the dungeon's entrance. If you did, make sure you destroy them using a hammer.
• If there's a Meteorite nearby, Meteor Heads will prevent the Cultists from spawning. Make sure to mine the meteorite away.
• The cultists won't spawn while you are in the dungeon. To be sure, you can wait near the World Spawn Point, or in the jungle, which are guaranteed to be far enough away.

If you did any of the above and they still didn't spawn, try restarting the world (by closing and opening it again). Finally, make sure no events are happening and no bosses are alive when checking if they spawned.

Also if there is a hole or you broke some of the entrance they won’t spawn. Try going deep into the dungeon and getting some bricks and fill it in