I created a normal world and traveled to the Lost Cities Dimension using the bed, diamond block and skulls. However when in the Lost Cities Dimension I cannot use a regular bed to sleep through the night.

In general, dimensions that aren't the Overworld don't let you sleep in them, so I believe this is intentional. @McJty can you confirm?

Ah, that does makes sense tbh.

I've also noticed I cannot make a Nether Portal. Would this come under the same rule as not sleeping in other dimensions?